Photonic microwave frequency downconversion with independent multichannel phase shifting and zero-intermediate-frequency (IF) receiving via an integrated polarization multiplexing dual-parallel Mach-Zehnder modulator (MZM) is proposed. Based on the ideas of optical frequency shift and polarization multiplexing, the radio frequency (RF) signal is frequency downconverted to multichannel IF signals with the phases independently and arbitrarily tuned by adjusting the polarization controllers or even frequency downconverted to baseband directly by choosing two quadrature channels. In the simulation, the gain of our proposed frequency downconversion system is higher than that of the conventional two cascaded MZMs' system, and the phase shift with the range of 360° can be obtained concurrently. Furthermore, 2.5 Gbit/s RF vector signals centered at 10 GHz with different modulation formats are successfully demodulated.