Accurate and stable wind speed forecasting is essential for the planning, scheduling and control of wind energy generation and conversion in wind power industry. In this paper, a novel nonlinear hybrid model aiming at improving prediction performance of wind speed called LSTMDE-HELM is presented by using Long Short Term Memory neural network (LSTM), Hysteretic Extreme Learning Machine (HELM), Differential Evolution algorithm (DE), and nonlinear combined mechanism. First, to enhance the performance of Extreme Learning Machine (ELM), a biological neural system property called hysteresis is embedded into neuron activation function of ELM. Second, as there isn't a clear knowledge to set the number of hidden layers in LSTM and neurons count in each hidden layer, DE is introduced to optimize these numbers by minimizing a weighted objective function for keeping balance between learning performance and model complexity. Finally, the forecasting results of each predictor in LSTMDE-HELM are aggregated by a novel nonlinear combined mechanism composed of LSTM network and also the DE is used to optimize this LSTM. The proposed nonlinear hybrid model is employed on the data gathered from a wind farm in Inner Mongolia, China. Two forecasting horizons i.e., ten-minute ahead (utmost short term) and one-hour ahead (short term) are adopted for experiments. Empirical results fully demonstrate the superiority of the proposed hybrid model compared with other models in terms of four performance indices and statistical tests.