In order to study the performance of the photonic microwave signal generated by a semiconductor laser (SL) under optical injection, based on the rate equation of SL and the fiber Bragg grating (FBG) filter theory, the optical spectra, power spectra, and linewidth under different injection parameters were obtained by numerical simulation and theoretical analysis, and the effect of the feedback parameters on the microwave linewidth was also studied. Considering that the generated microwave signal has wide linewidth, a FBG optical feedback was further introduced to narrow the microwave linewidth. The results show that, for the SL subject to optical injection only, the microwave frequency can be continuously tuned and the microwave intensity can be maximized by changing the injection parameters; the microwave linewidth gradually decreases with the increase of feedback strength. Through properly adjusting the feedback parameters, the microwave linewidth can be compressed below 10kHz. The results can provide a theoretical reference for the application of semiconductor laser in the photonic microwave signals generation.