In this paper, a photonic scheme to generate a frequency-quadrupled microwave signal with full-range 360° tunable phase shift is proposed and experimentally demonstrated. Pure ±2nd-order sidebands with the carrier suppressed are generated by a dual-parallel Mach-Zehnder modulator. The two sidebands are separated by a fiber Bragg grating with the polarization state of one sideband rotated by 90 deg via a Faraday rotating mirror and then recombined to obtain a pair of orthogonally polarized wavelengths. The two orthogonally polarized optical sidebands are aligned into the same polarization direction by using a polarizer (Pol). Finally, a radio frequency (RF) signal with frequency quadrupling of a local oscillator signal is obtained by beating the ±2nd-order sidebands at a photodetector. The phase θ of the frequency-quadruped RF signal can be independently and arbitrarily adjusted from 0° to 360° through control of the polarization direction. Experiments are carried out to demonstrate the scheme, and frequency-quadrupled microwave signals at 12 GHz and 16 GHz are generated. A continuous phase shift from 0° to 360° of the frequency-quadrupled signal at 12 GHz is also verified. The proposed scheme not only has the merits of large operation bandwidth and simple structure but also can be extended to multi-channel applications.