Using the rate equation of quantum dot laser (QDL) and the filtering model of fiber Bragg grating (FBG), the property of the photon microwave signals generated by a QDL subject to optical injection and FBG optical feedback is numerically investigated. The quality of the microwave signals is judged using optical spectrum, frequency spectrum, and linewidth techniques. The results show that for the fixed frequency detuning, the microwave frequency is robust to injection intensity and the microwave intensity first increases and then decreases with the increase of injection intensity. Considering that the microwave linewidth generated by optical injection is about 0.5 MHz, which is relatively wide, FBG filtering optical feedback is introduced to narrow the microwave linewidth. It is found that by adjusting the feedback parameters appropriately, the microwave linewidth can be compressed to around 1 kHz, and the linewidth compression effect is obvious. The research results can provide theoretical support for the application of the QDL in photogenerated microwaves.