A widely tunable narrow-linewidth photonic microwave generation scheme based on the period-one dynamics of an optically injected semiconductor laser combined with optoelectronic loops is proposed and experimentally demonstrated. The results show that the optical injection first drives the laser into period-one dynamics so that its intensity oscillates at a microwave frequency, which can be widely and continuously tuned in the range from 8 GHz to 67 GHz. A single sideband photonic microwave generation at 24.3 GHz is demonstrated with a proper injection condition. By using optoelectronic loops, the linewidth of the photonic microwave is effectively reduced from 8.6 MHz to 30 kHz and a signal to noise ratio above 40 dB is obtained.