"I'm Not Giving You Up" is a 1996 song by Cuban American singer and songwriter Gloria Estefan, released as the third single from her seventh studio album, Destiny (1996).

AllMusic editor Stephen Thomas Erlewine said that it "rank with her finest work", with the other album tracks "Reach" and "Higher".

[1] Larry Flick from Billboard noted that "the pace drops to a seductive and percussive shuffle, allowing her to stretch her lovely voice and perform with affecting emotion.

Swathed in fragile acoustic guitars and caressing strings, the chorus is impossible to shake from the mind after one listen."

[6] A reviewer from Music Week rated it four out of five, calling it "a smoochie ballad which should do well for Christmas", adding, "Expect a hit.