Considering the disadvantage of the algorithms based on statistics, a novel algorithm based on complex Hopfield neural network with amplitude-phase-type hard-multistate-activation-function (CHNN-APHM) is proposed to detect M-ary quaternary phase shift keying (MPSK) signals blindly. An amplitude-phase-type hard-multistate-activation-function is constructed. The stabilities of the CHNN-APHM with asynchronous and synchronous operating mode are also analyzed separately. While the weighted matrix of CHNN-APHM is constructed by the complementary projection operator of received signals, the problem of quadratic optimization with integer constraints can be successfully solved with the CHNN-APHM, and the MPSK signals are blindly detected. Simulation results show that the algorithm reaches the real equilibrium points with shorter received signals and if is applicable for channel with common zeros.