We present a new measurement of CP-violation parameters in B0→KS0π0γ decay based on a sample of 275×106 BB̄ pairs collected at the Υ(4S) resonance with the Belle detector at the KEKB energy-asymmetric e+e- collider. One of the B mesons is fully reconstructed in the B0→KS0π0γ decay. The flavor of the accompanying B meson is identified from its decay products. CP-violation parameters are obtained from the asymmetry in the distribution of the proper time intervals between the two B decays. We obtain SKS0π0γ=-0.58-0.38+0.46(stat)±0.11(syst) and AKS0π0γ=+0.03±0.34(stat)±0.11(syst), for the KS0π0 invariant mass covering the full range up to 1.8GeV/c2. We also measure the CP-violation parameters for the case B0→K*0(→KS0π0)γ and obtain SK*0γ=-0.79-0.50+0.63(stat)±0.10(syst) for AK*0γ fixed at 0. © 2005 The American Physical Society.