We report a measurement of time-dependent CP violation in B0→KS0π0π0 decays using a data sample of 772×106 BB pairs collected by the Belle experiment running at the ?(4S) resonance at the KEKB e+e- collider. This decay proceeds mainly via a b→sdd "penguin" amplitude. The results are sin2φ1eff=0.92-0.31+0.27 (stat.) ±0.11 (syst.) and A=0.28±0.21 (stat.) ±0.04 (syst.), which are the most precise measurements of CP violation in this decay mode to date. The value for the CP-violating parameter sin2φ1eff is consistent with that obtained using decay modes proceeding via a b→ccs "tree" amplitude.