Wind energy has received more and more attention around the world since it is a kind of clean, economical and renewable energy. However, the strong randomness of the wind speed makes wind power difficult to integrate into the power grid. Obtaining reliable high-quality wind speed prediction results is very important for the planning and application of wind energy. In this study, Shared Weight Long Short-Term Memory Network (SWLSTM) is proposed to decrease the number of variables that need to be optimized and the training time of Long Short-Term Memory Network (LSTM) without significantly reducing prediction accuracy. Furthermore, a new hybrid model combined SWLSTM and GPR, called SWLSTM-GPR, is proposed to obtain reliable wind speed probabilistic prediction result. SWLSTM-GPR is applied to four wind speed prediction cases in Inner Mongolia, China and compared with the state-of-the-art wind speed prediction methods from four aspects: point prediction accuracy, interval prediction suitability, probability prediction comprehensive performance and training time. The reliability test of SWLSTM-GPR guarantees that the prediction results are reliable and convincing. The experimental results show that SWLSTM-GPR can obtain high-precision point prediction, appropriate prediction interval and reliable probabilistic prediction results with shorter training time on the wind speed prediction problems.