For polarization multiplexed quadrature phase shift keying (PM-QPSK) coherent receiver system, a modified optical-signal-noise-ratio (OSNR) monitoring method based on high order statistical moment is presented. The calibration value of different modulation formats and the tolerance of residual chromatic dispersion (CD) and polarization mode dispersion (PMD) for the modified method are investigated. The proposed method is verified in numerical simulations in 112 Gb/s PM-QPSK coherent receiver system, and the OSNR measurement error is within 0.5 dB for all modulation formats with a wide range from 8 dB to 26 dB. The method also has a CD tolerance of 2800 ps/nm and a first-order PMD tolerance of 65 ps if the acceptable error is set to 0.5 dB when real OSNR is around 14 dB, and it is available in real time and in-band OSNR measurement of PM-QPSK coherent receiver system with lower computation complexity and without the requirement of extra monitoring device.