  We report the first measurement of CP-violation parameters in B^0 ->
K_S^0\rho^0\gamma decays based on 657 million B\bar B pairs collected with the
Belle detector at the KEKB asymmetric-energy collider. We measure the
time-dependent CP violating parameter S_{K_S^0\rho^0\gamma}= 0.11 +/-
0.33(stat.)^{+0.05}_{-0.09}(syst.). We also obtain the effective direct CP
violating parameter A_eff=0.05 +/- 0.18(stat.) +/- 0.06(syst.) for
m_{K_S\pi^+\pi^-}<1.8 GeV/c^2 and 0.6 GeV/c^2<m_{\pi^+\pi^-}<0.9 GeV/c^2.
