Optical coherent eavesdropping receiver model with limited bandwidth is established in Quadrature Phase Shift Keying(QPSK) system. And equivalent filter model about bandwidth limitation is given. The received signal model is present in the presence of limited bandwidth. The interferences of other symbols on current symbol are analyzed in detail with received signal constellation. Signal-to-noise ratio(SNR) is redefined and Bit Error Rate(BER) performance of receiver with limited bandwidth is derived based on Decision Aided Maximum Likelihood(DAML) phase estimation. The optimum sampling timing offset and bandwidth are also analyzed. Simulation results show that the maximum SNRs per bit we defined correspond to the minimum BER under different bandwidth. The optimum sampling timing offset and bandwidth are different with different type of filter, but the optimum ones can be found by SNR we defined. And with Optical Signal-to-Noise Ratio(OSNR) increasing, the performance of DAML phase estimation receiver is degraded by bandwidth limitation.