A novel complex multi-valued discrete Hopfield neural network (CMDHNN) is proposed in this paper. A multi-valued discrete activation function and a new energy function for CMDHNN are constructed. The stabilities for multi-valued CMDHNN with asynchronous and synchronous operating modes are also analyzed seperately. The special energy functions own the ability to describe the dynamic characteristics of CMDHNN which the energy functions of existing references cannot explain. Meantime, these energy functions can make the true source signal vector correspond to the minimum point of the energy function of CMDHNN. Furthermore, to verify effectiveness of CMDHNN, the weighted matrix of CMDHNN is constructed by the specific cost function for the blind detection of signals. Simulation results show that the proposed CMDHNN can be used to blindly detect the dense MQAM constellation signals with shorter received signals and the global minimal value of the CMDHNN energy function is verified.