A simple photonic approach to generating and anti-dispersion transmitting the quaternary phase-coded microwave waveforms is proposed and experimentally demonstrated. In this approach, an integrated dual-polarization binary phase shift keying (DP-BPSK) modulator is adopted and driven by two parallel pre-encoding signals as well as two RF inputs with 90-deg phase shift. By simply presetting the bias voltages on the DP-BPSK modulator, the phase-coded microwave signals with desired quadrature phase shifts and the immunity to dispersion-induced power fading can be obtained. A complete theoretical analysis on operation principle is presented. Experiments on the generation and anti-dispersion transmission of the 1 Gb/s quaternary phase-coded waveforms with the center frequencies of 6 or 7 GHz over 10 km SMF are successfully carried out. The proposed system can achieve the waveforms with multiple phase coded formats and transmit them over long-distance optical fiber without dispersion-induced power fading. Besides, it also features simple architecture, excellent reconfigurability, better Doppler tolerance and sensitivity of objective recognition, which is highly desirable in modern radar networks based on optical fiber transmission.