GPS accuracy is affected by multiple factors, such as satellite clock error, atmospheric delay and multipath fading. Traditionally, develop an algorithm to increase GPS accuracy requires complicated analytical modeling on each error source. Instead, this paper aims to present an approach to improve the accuracy by utilizing deep learning technique. A Long Short-Term memory (LSTM) based prediction method is presented to predict the GPS errors. A well trained model can learn and detect the underlying patterns of the GPS errors in the past time series and thus predict the future errors. Data smoothing preprocess is performed by a digital filter, which is designed and integrated into our approach, this preprocess increases the accuracy and the stability of the system by reducing the impact of unpredictable random noise. The system is set for 10 future steps prediction, with the performances been evaluated by comparing with traditional prediction models. Based on our experimental results, the overall prediction accuracy is increased by 16%, and 37.7% at the furthest prediction step.