  We present results of a study of the charmless vector-vector decays B^0 ->
K^{*0} rho^0 and B^+ ->K^{*0} rho^+. The results are based on a 140 fb^{-1}
data sample collected by the Belle detector at the KEKB asymmetric e^+e^-
collider. We obtain the branching fraction B(B^+ -> K^{*0} rho^+)=(6.6 +-
2.2(stat.) +- 0.8 (syst.)) x 10^{-6}, and set upper limits on the branching
fractions B(B^0 -> K^{*0} rho^0)<2.6 x 10^{-6} and B(B^0 -> f_0(980)
K^{*0})<5.2 x 10^{-6}. We also perform a helicity analysis of the rho and K^*
vector mesons in the decay B^+ -> K^{*0} rho^+, and obtain the longitudinal
polarization fraction R_0(B^+ -> K^{*0} rho^+)=0.50 +-
0.19(stat.)+0.05-0.07}(syst.).
