In this paper, we study channel tracking for the wireless energy transfer (WET) system, which is practically a very important, but challenging problem. Regarding the time-varying channels as a sequence to be predicted, we exploit the recurrent neural network (RNN) technique for channel tracking. Particularly, combining the deep long short-term memory (LSTM) RNN with the deep feedforward neural network, we develop a novel channel tracking scheme for the WET system, which estimates the channel state information (CSI) at the energy transmitter based on the previous CSI estimates, and the current and previous harvested energy feedback information from the energy receiver. Numerical results demonstrate the superior performance and effectiveness of the proposed scheme.