The effect of optical feedback on stability and linewidth of photonic microwave generated in an optically injected single-mode vertical-cavity surface-emitting laser has been investigated in both cases of single feedback and double feedback. The stability of photonic microwave is quantified by measuring the microwave frequency range using the long sweep time of the radio frequency spectrum analyzer. The effect of the feedback phase on the side peaks in the single feedback has also been studied. The experimental results show that both single feedback and double feedback can reduce the linewidth of photonic microwave and improve its stabilization. A narrow linewidth photonic microwave spectrum with suppressed side peaks has been achieved in single feedback configuration at the optimal feedback phase condition. The simulated results using the spin-flip model confirm that side peaks suppression in single optical feedback configuration is sensitive to the feedback phase. For non-optimal feedback phase conditions, single optical feedback can generate many side peaks which are related to external cavity. These side peaks can be suppressed by introducing the second feedback.