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We present a new stochastic learning machine for speech separation based on the variational recurrent neural network (VRNN). This VRNN is constructed from the perspectives of generative stochastic network and variational auto-encoder. The idea is to faithfully characterize the randomness of hidden state of a recurrent neural network through variational learning. The neural parameters under this latent variable model are estimated by maximizing the variational lower bound of log marginal likelihood. An inference network driven by the variational distribution is trained from a set of mixed signals and the associated source targets. A novel supervised VRNN is developed for speech separation. The proposed VRNN provides a stochastic point of view which accommodates the uncertainty in hidden states and facilitates the analysis of model construction. The masking function is further employed in network outputs for speech separation. The benefit of using VRNN is demonstrated by the experiments on monaural speech separation.