We present a measurement of the time-dependent CP asymmetry for the neutral B-meson decay into the CP = +1 final state K-S(0)pi(0)pi(0), with K-S(0)->pi(+)pi(-). We use a sample of approximately 227 million B-meson pairs recorded at the Upsilon(4S) resonance with the BABAR detector at the PEP-II B-Factory at SLAC. From an unbinned maximum likelihood fit, we extract the mixing-induced CP-violation parameter S=0.72 +/- 0.71 +/- 0.08 and the direct CP-violation parameter C=0.23 +/- 0.52 +/- 0.13, where the first uncertainty is statistical and the second systematic.