A new dual-function photonic microwave signal processing structure that has the ability to realize both frequency up/down conversion and RF/IF phase shifting, is presented. In the proposed signal processor, a dual-polarization dual-parallel Mach Zehnder modulator (DP-DPMZM) is used to generate an orthogonally polarized single RF/IF signal and LO modulation sideband without an optical carrier. The optical phase difference between the two sidebands can be controlled by controlling a DC voltage applied to a LiNbO3 electro-optic phase modulator that is connected after the DP-DPMZM. Beating between the two sidebands at a photodetector generates an RF/IF signal with a phase equal to the optical phase difference between the IF/RF signal and LO sidebands. The dual-function photonic microwave signal processor has a wide bandwidth and does not require a precise control of the laser wavelength. Experimental results demonstrate that a flat > -3 dB down/up conversion efficiency is achieved for an RF signal from 3.5 to 26.5 GHz and for an IF signal from 0.5 to 3 GHz, and a full 360° continuous phase shift of the output IF/RF signal.