The polarization-division multiplexing (PDM) technology is a practical method to double the transmission capacity, and the corresponding phase regeneration (PR) for PDM signals is meaningful and necessary to extend the transmission distance and increase the transparency for the phase-encoded PDM system. Those reported PDM PR schemes either utilized polarization-diversity technique or required special PDM format. In order to overcome these issues, the PR for the PDM phase-modulated signals is proposed and theoretically demonstrated in this paper, based on the vector dual-pump nondegenerate phase sensitive amplification (PSA). The theoretical model is established and the detailed characteristics are investigated to optimize the PR performance. Results show an obvious phase squeezing for the degraded 80 Gbit/s PDM differential phase-shift keying (DPSK) signals, and the error vector magnitude (EVM) of the regenerated signals on dual polarization states can be improved from 22.58% and 21.39% to 4.57% and 4.63%, respectively. Furthermore, the applicability of the proposed scheme for PDM quaternary-phase shift keying (QPSK) signals is investigated. The proposed scheme can be useful and promising in current PDM based coherent fiber-optic communication.