A study on power market price forecasting by deep learning is presented. As one of the most successful deep learning frameworks, the LSTM (Long short-term memory) neural network is utilized. The hourly prices data from the New England and PJM day-ahead markets are used in this study. First, a LSTM network is formulated and trained. Then the raw input and output data are preprocessed by unit scaling, and the trained network is tested on the real price data under different input lengths, forecasting horizons and data sizes. Its performance is also compared with other existing methods. The forecasted results demonstrate that, the LSTM deep neural network can outperform the others under different application settings in this problem.