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 535x10(6) B(B) over bar 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)]x10(-4) for the branching fraction of B-0 -> 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 B-0 -> D+D- at the 4.1 sigma 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 3.2 sigma confidence level, in contradiction to standard model expectations.