A narrow-linewidth single-frequency photonic-microwave-generation scheme using an optically injected semiconductor laser with a filtered optical feedback has been proposed. The filtered feedback comes from a single feedback loop, which includes a narrow bandpass filter. With the filtered feedback, the linewidth of the generated microwave can be significantly reduced from 22.4 MHz to 9.0 kHz, with the side peaks suppression of 28 dB. The proposed scheme shows superior performance compared to the conventional single-feedback configuration in terms of linewidth reduction and side peaks suppression. The proposed scheme also achieves better results compared to the complex dual-feedback setting. The mechanism for a better performance of filtered optical feedback is that the filtered feedback can effectively limit the external cavity modes and stabilize the period-one dynamics. In addition, the microwave linewidth decreases with the increase of the filter width until the optimized filter width is reached. Furthermore, the linewidth reduction and the side peaks suppression of a photonic microwave using filtered optical feedback is relatively insensitive to the frequency detuning between the filter center frequency and the free-running frequency of the semiconductor laser.