We report measurements of the branching fraction and CP violation parameters in B(0)-->D+ D- decays. The results are based on a data sample that contains 535 x 10(6) BB pairs collected at the Upsilon(4S) resonance, with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain [1.97+/-0.20(stat) +/- 0.20(syst)] x 10(-4) for the branching fraction of B0-->D+D-. The measured values of the CP violation parameters are S=-1.13+/-0.37+/-0.09, A=0.91+/-0.23+/-0.06, where the first error is statistical and the second is systematic. We find evidence of CP violation in B0-->D+D- at the 4.1sigma confidence level. While the value of S is consistent with expectations from other measurements, the value of the parameter A favors large direct CP violation at the 3.2sigma confidence level, in contradiction to standard model expectations.