The single-channel blind separation of GMSK(Gaussian Minimum Shift Keying) mixing signals is researched. The GMSK mixing signals can not be separated by the Per-Survivor Processing (PSP) algorithm directly, therefore, linear approximation processing of the GMSK signal is considered, which enables GMSK signal to be separated by the PSP algorithm. This algorithm separates the GMSK mixing signals by maximum likelihood estimation in the joint space of the symbol sequential and the channel parameters, reserves the best path and outputs the symbol pairs to get the separated signals. Simulation results show that the bit error rate performance produced by the PSP algorithm on separating the GMSK mixing signals is slightly better than that produced by the particle filtering algorithm; and the complexity of the proposed PSP algorithm is much smaller.