We report a measurement of CP violating asymmetries in B-0 ((B-0) over bar) -> (K+K-KS0) decays with a time-dependent Dalitz approach. This analysis is based on a data sample of 657 x 10(6) B (B) over bar pairs accumulated at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+) e(-) collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct CP violation parameters phi(eff)(1) and A(CP) are obtained for B-0 -> phi(1020)K-S(0), B-0 -> f(0)(980)K-S(0), and other B-0 -> (K+K-KS0) decays. We find four solutions that describe the data. There are phi(eff)(1) (B-0 -> phi(1020)K-S(0)) = (32.2 +/- 9.0 +/- 2.6 +/- 1.4); phi(eff)(1)(B-0 -> phi(1020)K-S(0)) = 26.2 +/- 8.8 +/- 2.7 +/- 1.2); phi(eff)(1)(B-0 phi(1020)K-S(0)) = (27.3 +/- 8.6 +/- 2.8 +/- 1.3); and phi(eff)(1)(B-0 -> phi(1020)K-S(0)) = (24.3 +/- 8.0 +/- 2.9 +/- 5.2). The values for the CP violating phase in B-0 -> phi(1020)K-S(0) are similar, but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent phi(eff)(1) values for all three B-meson decay channels and none of them deviates significantly from the values measured in B -> (c (c) over bar )K-0 decays with the currently available statistics. In addition, we find no significant direct CP violation.