Measurements are presented of the CP violation observables S and C in the decays of B-0 and (B) over bar (0) mesons to the J/psi K-S(0) final state. The data sample corresponds to an integrated luminosity of 3.0 fb(-1) collected with the LHCb experiment in proton-proton collisions at center-of-mass energies of 7 and 8 TeV, and contains a total of 41 560 selected B-0 and (B) over bar (0) decays. The analysis of the time evolution of these decays yields S = 0.731 +/- 0.035(stat) +/- 0.020(syst) and C = -0.038 +/- 0.032(stat) +/- 0.005(syst). In the standard model, S equals sin(2 beta) to a good level of precision. The values are consistent with the current world averages and with the standard model expectations.