Rein Rannap (born October 6, 1953 in Tallinn) is an Estonian composer and pianist.
Since 1968, Rannap has given numerous public piano performances. Rannap has been active in management and composition for Ruja, Noor-Eesti and Hõim.
Rannap gave his first solo concert in 1968. Since that time, he has performed piano concerts in many regions of the (former) Soviet Union, a number of European countries, as well as Australia and United States. In 1997 and 1999, he toured Estonia under the Klaver tuleb külla (Estonian for The Piano Comes to Visit) programme, transporting his piano to various churches in Estonia for the performances.