Even when Indra Nooyi reached the top of one of the biggest companies in the world, the former PepsiCo Inc. boss says she had to contend with sexism in her own board room, where a couple of male directors routinely talked over her.

In her new memoir, “My Life in Full: Work, Family, and Our Future,” she recounts how, as one of India’s first female M.B.A. graduates, she rose to become chairman and chief executive of the soda-and-snacks giant. She describes encountering a business climate that was inhospitable for families in...

Even when Indra Nooyi reached the top of one of the biggest companies in the world, the former PepsiCo Inc. boss says she had to contend with sexism in her own board room, where a couple of male directors routinely talked over her.

In her new memoir, “My Life in Full: Work, Family, and Our Future,” she recounts how, as one of India’s first female M.B.A. graduates, she rose to become chairman and chief executive of the soda-and-snacks giant. She describes encountering a business climate that was inhospitable for families in which both parents worked. Ms. Nooyi says she and her husband struggled to find reliable child care and cobbled together informal arrangements, leaning on her mother and flying relatives over from India for monthslong stints.

Many of these problems persist today in American business, says Ms. Nooyi, 65, who retired from PepsiCo in 2018 and is mulling her next career move. She is now advocating for policies like paid parental leave, a national child care system, flexible work schedules and remote work arrangements—the kind of support that she says could have allowed her to be more present for her two daughters when they were young. Below, an edited interview:

The Wall Street Journal: How would your life have been different if you had had access to flexible work, remote work or on-site child care?

Ms. Nooyi: Had I had technology to keep in touch with my kids and been allowed to work flexibly, I would have not missed some of the important parts of my children growing up. Even though we had family coming from India coming to help us, there were tensions, there were challenges, there were scheduling issues. We had to struggle through all of that. It would have been much easier for my husband and me to take turns at working from home.

WSJ: Your description of multigenerational living resonated with me, because my family lived that way during the pandemic.

Ms. Nooyi: That is an adjustment, because your parents believe they know a little bit more about bringing up kids, that they’ve got more experience. But we want a different model to bring up the kids, and oh, God, don’t even get me started. I’ve got to say everybody is right. You tell your husband, “shush,” quietly. You’ve got to tell your mother, “shush,” quietly. That’s how you fine-tune your diplomatic skills.

WSJ: You write that you faced sexist behavior from a couple of your own board members. What advice do you have for women executives in similar situations today?

Ms. Nooyi: I had one of the most supportive and amazing boards. But a couple members would feel free to talk over me or interrupt me before I finished. One of the board members would always say to me, “I wouldn’t quite say it that way,” and when I asked him how he would put it, he would repeat exactly what I said. I’m like, “Give me a break.”

If leaders observe a behavior that’s not quite OK, they should call it out right there and say, “Look, let’s make sure that we don’t talk over her.” I’m also hoping that a critical mass of women will help each other through these situations, because when you’re the only woman in the room, it’s very hard to try to change behavior on your own.

WSJ: You suggest a mandatory retirement age for corporate directors and a maximum tenure of 15 years. Do you think a big shake-up is necessary?

Ms. Nooyi: What we need to do is to add capability to the board which brings in a representation of the working woman’s voice so that those issues of family and women are also core to boardroom discussions. You can expand the board, and if you don’t do that, then you’ve got to figure out how to retool the existing room.

WSJ: Twice in your career, you tendered your resignation when your bosses failed to put an end to sexist behavior. In 1994 at engineering company ABB, you write that your boss regularly called you “honey.” And in 1996 when you were a top strategist at PepsiCo, you write that male colleagues insulted you in meetings when you presented forecasts that differed from theirs—and no one backed you up. What did you learn from those experiences?

Ms. Nooyi: The first time, I said, “I’m leaving,” and I left. The second time, PepsiCo changed rapidly and said it isn’t going to happen again. It was not a threat and I wasn’t asking for anything. I’m just telling you, “If you don’t give me respect, I’ll take my skills someplace else.” That was a major turning point in my time at PepsiCo.

WSJ: Because you were treated with more respect after that?

Ms. Nooyi: Yeah. A couple of people who would constantly put me down realized that they were doing things wrong because [then-CEO Roger Enrico] called them out. The tone at the top, which was a little silent for a while, changed, called out the bad behavior.

WSJ: You write that you were dismayed by the headlines that there was no female contender to replace you at PepsiCo when you stepped down. Could you talk about how you tried to groom female executives at the company?

Ms. Nooyi: We groomed a lot of leaders. But PepsiCo is a gigantic global company and somebody who is senior middle management at PepsiCo is a prime candidate to be the CEO of a big geographical business of a large company or a medium-size public company. They would get constantly raided to go off and run these companies.

So we lost some good women to that. Look at what Lauren Hobart is doing at Dick’s Sporting Goods. She’s one of us, absolutely terrific performance. Look at what Ann Mukherjee is doing [at Pernod Ricard ], what Debra Crew is doing [at Diageo ]. These were all great women executives at Pepsi. I’m still in touch with all of them, and it’s an amazing sisterhood. But I feel better because we provided talent for the corporate world in general.

WSJ: When you were CFO in 2000, you learned that you were not being paid on par with the men around you. What can companies do to address the problem of pay inequality?

Ms. Nooyi: I never thought about pay until Steve Reinemund became CEO and made a big adjustment to my base salary and gave me a big stock option grant. We lived way below our means because we were brought up a certain way, and so asking for a raise was just not in our vocabulary.

In today’s world, people shouldn’t have to ask for pay parity. I hope we have now progressed to a point where there’s enough sensitivity about equal pay for the same jobs that HR departments and companies are looking at this metric regularly and calibrating to make sure that they’re paying every person the same for the same job.

Look, we’ve come a long way since 2000. I would have liked for progress to have been faster, but it’s happening, and that’s what we should celebrate.

Write to Jennifer Maloney at jennifer.maloney@wsj.com