The organization behind the Grammy Awards, which has been under scrutiny over the representation of women, has a new boss.

The Recording Academy said on Wednesday that its new president and chief executive would be Deborah Dugan, the former chief of Red, the nonprofit group co-founded by Bono of U2 that works to combat AIDS and other diseases in Africa.

Ms. Dugan, the first woman to hold the top job at the 62-year-old academy, will take command of an organization that offers artists prestige and valuable TV time, yet has been embattled on many fronts. Last year, Neil Portnow, Ms. Dugan’s predecessor, was widely condemned for saying women in music should “step up” to advance their careers.

In response, some female executives demanded that Mr. Portnow resign, and the academy appointed a task force to examine the organization’s “various barriers and unconscious biases.”