An all-optical photonic microwave phase shifter that can realize a continuous 360° phase shift over a wide frequency range is presented. It is based on the new concept of controlling the amplitude and phase of the two RF modulation sidebands via a Fourier-domain optical processor. The operating frequency range of the phase shifter is largely increased compared to the previously reported Fourier-domain optical processor based phase shifter that uses only one RF modulation sideband. This is due to the extension of the lower RF operating frequency by designing the amplitude and phase of one of the RF modulation sidebands while the other sideband is designed to realize the required RF signal phase shift. The two-sideband amplitude-and-phase-control based photonic microwave phase shifter has a simple structure as it only requires a single laser source, a phase modulator, a Fourier-domain optical processor and a single photodetector. Investigation on the bandwidth limitation problem in the conventional Fourier-domain optical processor based phase shifter is presented. Comparisons between the measured phase shifter output RF amplitude and phase responses with theory, which show excellent agreement, are also presented for the first time. Experimental results demonstrate the full -180° to + 180° phase shift with little RF signal amplitude variation of less than 3 dB and with a phase deviation of less than 4° over a 7.5 GHz to 26.5 GHz frequency range, and the phase shifter exhibits a long term stable performance. © 2015 Optical Society of America.