We have investigated chaotic synchronization in the generalized sense for the degenerate optical parametric oscillator (DOPO). The numerical results show that two unidirectional coupling DOPOs in chaos can be completely phase synchronization or anti-phase synchronization with a suitable coupling coefficient under which the maximum condition Lyapunov exponent (MCLE) is negative. Phase synchronization and anti-phase synchronization of chaos can be realized through positive and negative coupling. On the other hand, the different synchronization states depend on the coupling types used in the DOPO systems.