Wind energy, as renewable energy, has drawn the attention of society. The use of wind power generation can reduce the pollution to the environment and solve the problem of power shortage in offshore islands, grassland, pastoral areas, mountain areas, and highlands. Wind speed forecasting plays a significant role in wind farms. It can improve economic and social benefits and make an operation schedule for wind turbines in large wind farms. At present, researchers have proposed a variety of methods for wind speed forecasting; artificial neural network (ANN) is one of the most commonly used methods. This paper proposes a combined model based on the existing artificial neural network algorithms for wind speed forecasting at different heights. We first use the wavelet threshold method to the original wind speed data set for noise reduction. After that, the three artificial neural networks, extreme learning machine (ELM), Elman neural network, and Long Short-Term Memory neural network (LSTM), are applied for wind speed forecasting. In addition, variance reciprocal method and society cognitive optimization algorithm (SCO) are used to optimize the weight coefficients of the combined model. In order to evaluate the forecasting performance of the combined model, we select wind speed data at three heights (20m, 50m, and 80m) in National Wind Technology Center M2 Tower. The experimental results show that the forecasting performance of the combined model is better than the single model, and it has a good forecasting performance for the wind speed at different heights.