[3] Parra turned professional for the first Colombian cycling team, Café de Colombia, in 1985.

He was a professional from 1985 to 1992 and won stages in the Tour de France and Vuelta a España.

While Herrera won stages and the King of the Mountains competitions in the grand tours, Parra could contend for the overall classification.

His greatest achievements were a third place in the 1988 Tour de France, highest placing of a South American for 25 years, until his countryman Nairo Quintana finished second in the 2013 Tour de France, and, in the following year in the Vuelta a España, finishing second to Pedro Delgado at 35 seconds.

Humberto rode for three years for Kelme while Iván won 2 stages of the 2005 Giro d'Italia.