Abstract: Training the stochastic feedforward neural network with expectation maximization (EM) algorithm has many merits such as reliable global convergence, low cost per iteration and easy programming. A new algorithm named A-EM (annealing-expectation maximization) based on the EM algorithm is proposed for training the stochastic feedforward neural network. The A-EM algorithm computes the condition probability of the hidden variable in the network system through the maximum entropy principle of the thermodynamics. It can reduce the influence of the initial value on the final resolution by simulating the annealing process and introducing the temperature parameter. This algorithm can not only keep the merits of the original EM, but also facilitate the results converge to the global minimum. The convergence of the algorithm is proved and its correctness and validity is verified by experiments.