A new photonic microwave phase shifter that can achieve a full 360° phase shift with very little RF signal amplitude variation, and which can operate over very wide frequency range, is presented. It is based on controlling the amplitude and phase of the optical carrier and the two RF modulation sidebands via the dc bias voltages to a dual-parallel Mach-Zehnder modulator (DPMZM). It has a simple structure, only requiring a single laser, modulator, and photodetector. A continuous 360° RF phase shift without changes in the RF signal amplitude is obtained by controlling the dc bias voltages of the DPMZM. Experimental results demonstrate a very wideband operation of the RF phase shifter over an 8:1 frequency range from 2 to 16 GHz, a continuous 0-360° RF phase shift with very low amplitude variation of <3 dB of over the entire frequency band, and with a phase deviation standard deviation of <2°.