More recently, wind speed forecasting as an effective computing technique currently plays an important role in advancing industry informatics, while dealing with those issues of control and operation for renewable power systems. However, it is facing some increasing difficulties to handle the large-scale dataset generated in these forecasting applications, with the purpose of ensuring stable computing performance. In response to such limitation, this article proposes a more practical approach through the combination of extreme learning machine (ELM) method and deep learning model. ELM as a novel computing paradigm enables the neural network- (NN-) based learning to be achieved with fast training speed and good generalization performance. The stacked ELM (SELM) is an advanced ELM algorithm under deep learning framework, which works efficiently on memory consumption decrease. In this article, an enhanced SELM is accordingly developed via replacing the Euclidean norm of the mean square error (MSE) criterion in ELM with the generalized correntropy criterion to further improve the forecasting performance. The advantage of the enhanced SELM with generalized correntropy to achieve better forecasting performance mainly relies on the following aspect. Generalized correntropy is a stable and robust nonlinear similarity measure while employing machine learning method to forecast wind speed, where the outliers may exist in some industrially measured values. Specifically, the experimental results of short-term and ultra-short-term forecasting on real wind speed data show that the proposed approach can achieve better computing performance compared with other traditional and more recent methods.