We report the first observation of the charmless vector-vector decay process B-/+-->rho(-/+)rho(0). 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 B(B-/+-->rho(-/+)rho(0))=[31.7+/-7.1(stat)+3.8-6.7(syst)]x10(-6). An analysis of the rho helicity-angle distributions gives a longitudinal polarization fraction of Gamma(L)/Gamma=0.95+/-0.11(stat)+/-0.02(syst). We also measure the direct-CP-violating asymmetry A(CP)(B-/+-->rho(-/+)rho(0))=0.00+/-0.22(stat)+/-0.03(syst).