Wind power plays a leading role in the development of renewable energy. However, the random nature of wind turbine power and its associated uncertainty create challenges in dispatching this power effectively in the power system, which can result in unnecessary curtailment of the wind turbine power. Improving the accuracy of wind turbine power forecasting is an effective measure for resolving such problems. This study uses a deep learning network to forecast the wind turbine power based on a long short-term memory network (LSTM) algorithm and uses the Gaussian mixture model (GMM) to analyze the error distribution characteristics of short-term wind turbine power forecasting. The LSTM algorithm is used to forecast the power and uncertainties for three wind turbines within a wind farm. According to numerical weather prediction (NWP) data and historical power data for three turbines, the forecasting accuracy of the turbine with the largest number of training samples is the best of the three. For one of the turbines, the LSTM, radial basis function (RBF), wavelet, deep belief network (DBN), back propagation neural networks (BPNN), and Elman neural network (ELMAN) have been used to forecast the wind turbine power. This study compares the results and demonstrates that LSTM can greatly improve the forecasting accuracy. Moreover, this study obtains different confidence intervals for the three units according to the GMM, mixture density neural network (MDN), and relevance vector machine (RVM) model results. The LSTM method is shown to have higher accuracy and faster convergence than the other methods. However, the GMM method has better performance and evaluation than other methods and thus has practical application value for wind turbine power dispatching.