Wind power forecasting (WPF) plays an important role in the planning, efficient operation, and security maintenance of power systems. A large number of hybrid models have been applied to WPF in the past two decades. Due to the rapid development of swarm intelligence algorithms, there is great potential for forecasting performance improvements by combining them with basic data-driven models for parameter optimization. In this study, a hybrid WPF method is proposed, which combines an extreme learning machine (ELM) and improved teaching-learning-based optimization (iTLBO), and incorporates a recursive feature elimination (RFE) method for feature selection. For WPF, appropriate feature combination is recognized from original input data using the RFE method, which helps facilitate understanding of the data pattern and defy the curse of dimensionality. To enhance the convergence speed and learning ability of the basic TLBO, four improvements are performed, and the obtained iTLBO algorithm is applied to optimize the parameters of the ELM model. Case study data came from a wind farm in Yunnan, China. The ERMSE, EMAE, and MAPE values of the proposed hybrid method are all lower than those of the comparison methods. The results demonstrate the superior forecasting performance that makes the hybrid method more applicable in real WPF applications.