To deal with the problem of polarization demultiplexing in coherent optical communication systems for probabilistically shaped scenes, this paper proposes a polarization demultiplexing algorithm based on independent component analysis and maximum likelihood estimation. Due to the independence between the signals, the polarization demultiplexing of signals can be realized by the independent component analysis. The iterative update based on maximum likelihood estimation is used to find the best separation matrix, which is the polarization demultiplexing matrix. The performance of the algorithm under different optical signal-to-noise ratios and the tolerance of the shaping intensity are simulated and analyzed. The results show that the proposed scheme can cope with different probabilistically shaped intensities, and can achieve good polarization demultiplexing in a large optical signal-to-noise ratio range. Compared with the constant modulus algorithm for standard signals, this scheme will not be affected by the shaping intensity. As the shaping intensity increases, the performance of the system can be improved.