A measurement of the decay time-dependent CP-violating asymmetry in B-s(0) -> phi phi decays is presented, along with measurements of the T-odd triple-product asymmetries. In this decay channel, the CP-violating weak phase arises from the interference between B-s(0) -(B) over bar (0)(s) mixing and the loop-induced decay amplitude. Using a sample of proton-proton collision data corresponding to an integrated luminosity of 3.0 fb(-1) collected with the LHCb detector, a signal yield of approximately 4000 B-s(0) -> phi phi decays is obtained. The CP-violating phase is measured to be phi(s) = -0.17 +/- 0.15(stat) +/- 0.03(syst) rad. The triple-product asymmetries are measured to be A(U) = -0.003 +/- 0.017(stat) +/- 0.006(syst) and A(V) = -0.017 +/- 0.017(stat) +/- 0.006(syst). Results are consistent with the hypothesis of CP conservation.