Synchronizations of semiconductor ring lasers are investigated numerically . When the frequency mismatch is -20GHz and the injection coefficient is greater than 2.5, the semiconductor ring lasers in two different configurations (open and closed loops) can all achieve good synchronizations with cross correlation coefficient above 0.95. The robustness of two schemes to frequency detuning with different injection coefficients are discussed and the results show the robustness of open loop structure are better than that of closed loop structure. The influences of internal parameters′ mismatches on the chaos synchronization are also studied. The synchronization of two structures can be optimized by choosing appropriate internal parameters. The correlation coefficient of closed loop increases from 0.96 to 0.99 (0.95 to 0.97 about open loop). At last the impacts of the feedback delay time and bias current on the synchronization in the closed loop structure are analyzed.