In order to study nonlinear dynamic characteristics of a semiconductor ring laser (SRL) under external cross-optical feedback, the time series and power spectra under various feedback parameters were obtained by numerical simulation based on the SRL rate equation, and the effect of feedback coefficient on chaotic bandwidth and time delay characteristics was studied. The results show that SRL exhibits a variety of dynamic states such as single period, multi-period, low-frequency anti-phase fluctuation and chaotic state under various external feedback parameters. The maximum chaotic bandwidth of 3.7GHz can be obtained with symmetric optical feedback, and the time delay characteristics of chaotic signals generated by time-asymmetric optical feedback are well suppressed. The results of this study can provide some theoretical reference for the practical application of SRLs.