Photonic microwave generation has attracted much attention in recent years due to its potential applications in various fields such as radio-over-fiber communication, signal processing and radar systems. So far, different photonic microwave generation schemes have been proposed and investigated, such as the optical heterodyne method based on the beat of two independent lasers with a certain wavelength difference, the external modulation method based on electro-optical modulator, the dual-mode beat method based on the monolithic dual-mode semiconductor lasers, and the optoelectronic microwave oscillator method based on optoelectronic feedback loops. These schemes have their own advantages and deficiencies. Unlike the above schemes, in this paper we propose an all optical scheme for generating high-quality microwave based on a 1550 nm vertical-cavity surface-emitting laser (1550 nm-VCSEL). For such a scheme, high frequency microwave can be obtained based on a 1550 nm-VCSEL subjected to external optical injection, where the polarization of the injected light is the same as that of the dominant mode of the free-running 1550 nm-VCSEL (named parallel-polarized optical injection) and its wavelength is adjusted to being close to the wavelength of the suppressed polarization mode of the free-running 1550 nm-VCSEL. With the aid of double optical feedback, the linewidth of the obtained microwave can be narrowed. In this work, firstly, the feasibility of microwave generation based on parallel-polarized optically injected 1550 nm-VCSEL is analyzed theoretically by using the spin-flip model. Next, a corresponding experimental system is constructed, and the performance of microwave generation is preliminarily investigated experimentally. The experimental results show that 30 GHz microwave signals could be obtained based on a parallel-polarized, optically injected 1550 nm-VCSEL under suitable injection parameters, but the linewidth of microwave signal is relatively wide (hundreds of MHz). Finally, after introducing double optical feedback, the linewidth of microwave signal can be reduced by more than two orders of magnitude and narrowed to less than 1 MHz, meanwhile the signal-noise ratio is larger than 40 dB. This work is helpful to develop relevant techniques to acquire high-performance narrow linewidth photonic microwave.