When John Browne ran BP, he kept his life as a gay man a secret. Had he been true to himself, Browne believes he would have been a much different leader.
Now he's chronicled his experience in a new book, "The Glass Closet: Why Coming Out is Good Business," and is encouraging corporate America to make it easier for gay workers to come out.
"If I replay my life, by leading BP without not actually telling people about myself, set up a great mirror, a great piece of glass between me and all the team. I was very reserved. Had I shown myself I believe I could have lead them in a very different way," Browne said in an interview with "Power Lunch."
"Authenticity is very important."
Browne, who was CEO of BP from 1995 to 2007, found his personal world and business world colliding in 2007 when an ex-boyfriend outed him in the press. He resigned as BP's CEO after 41 years with the company.
Being a closeted CEO "meant that I had to have two different lives—a public life and a private life—and I tried to make sure they never met. That was quite exhausting," Browne said.
He believes part of the problem is the conservative boardrooms of major corporations and noted that not one of the CEOs on the is known to be gay.
"When it comes to out gay CEOs, not rumors about them, but out gay CEOs, I think you have to get down to somewhere like 700 in the S&P list to find someone who's out," Browne said. "This is extraordinary. It cannot be right."
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He also called the comments by Texas Gov. Rick Perry, who compared homosexuality to alcoholism, "dangerous."
On Monday, Gov. Perry expanded on the topic, telling CNBC he doesn't necessarily condone what he referred to as the gay lifestyle, nor does he condemn it. He also said "I don't know" when asked if he believes in"reparative therapy" for gays and lesbians who want change sexual orientation through counseling. The idea was adopted as part of the Texas Republican Party's policy at its convention earlier this month.
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"It's not a choice," Browne said. "This is not preference, this is part of you, and to suggest anything that might create segregation or change of location as a result of sexuality is absolutely wrong."
Instead, corporations should encourage its employees to be authentic, because it will not only help morale but will boost the company's bottom line.
"You don't want people spending half their time worrying about half their life no one can see. You really want them to bring the whole person to work," Browne said. "And I think all studies seem to show having the right climate where people can be themselves improves productivity enormously—about 30 percent."
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—By CNBC's Michelle Fox. CNBC's Kerima Greene contributed to this report.