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A microwave photonic system that can realize frequency up- and down-conversion, multichannel phase shift, high conversion gain, and elimination of dispersion-induced power fading is proposed and experimentally demonstrated. The scheme is based on an integrated dual-polarization quadrature phase shift keying modulator that contains two dual parallel Mach-Zehnder modulators (X-DPMZM and Y-DPMZM). The X-DPMZM implements dual side band carrier suppression (DSB-CS) modulation of radio frequency signal, and the Y-DPMZM implements frequency shift of an optical carrier. They are combined in orthogonal polarizations to implement frequency up- and down-conversion. The polarization multiplexed signal will go through polarization controllers and polarizers to implement multichannel phase shift. In the experiment, the phase shift can be tuned independently over 360° in each channel. By suppressing the optical carrier, the conversion gain and LO isolation are improved by 20.5 dB and 51.26 dB, respectively, compared with conventional dual side band modulation scheme. In addition, the proposed scheme can achieve a spurious-free dynamic range (SFDR) of 103.6 dB·Hz^2/3.