A novel microwave photonic phase shifter based on dual-parallel Mach-Zehnder modulator (DPMZM) modulation sideband filtering is proposed. Within the structure of DPMZM, one optical path with a Mach-Zehnder modulator is adjusted to be maintained at the state of optical-carrier-suppressed double-sideband modulation, and the other optical path is used to introduce an adjustable phase shift of the optical carrier by simply controlling the direct current (DC) bias voltage. The output of DPMZM passes through a fiber Bragg grating (FBG) for filtering out one first-order sideband of the modulation. A wideband photodetector is used to convert the output of FBG to electronic microwave signal of adjustable phase shift. The experimental results show that the proposed microwave photonic phase shifter based on DPMZM modulation sideband filtering has the advantage of stable transmission characteristics with small amplitude fluctuation, fast phase tuning response, wide frequency band and a phase shift greater than 360°.