  We report the first observation of the charmless vector-vector decay process
B+ ->rho+ rho0. The measurement uses a 78 fb^{-1} data sample collected with
the Belle detector at the KEKB asymmetric e+e- collider operating at the
Upsilon(4S) resonance. We obtain a branching fraction of Br(B+ ->rho+
rho0)=(31.7+-7.1(stat.)+3.8-6.7(sys.))*10^{-6}. An analysis of the rho
helicity-angle distributions gives a longitudinal polarization of
Gamma_{L}/Gamma=(94.8+-10.6(stat.)+-2.1(sys.))%.
