Moses Martin, the couple's second child, was born during the weekend in New York City, the office of Paltrow's publicist, Stephen Huvane, said Monday. No other information was being released.
Paltrow, 33, won an Oscar for her role in 1998's "Shakespeare in Love." The British-born Martin, 29, is lead singer of Coldplay.
Their daughter, Apple, will be 2 on May 14.
After Apple's birth, Paltrow appeared on "The Oprah Winfrey Show" and said she didn't understand why people were making a big deal about her daughter's name. Paltrow said it was Martin who came up with Apple.
"It conjured such a lovely picture for me -- you know, apples are so sweet and they're wholesome and it's biblical -- and I just thought it sounded so lovely and clean," Paltrow told Winfrey.