Accurate and reliable wind speed forecasting (WSF) is crucial for wind power systems. As one of the effective forecast methods, machine learning (ML) methods are employed for wind speed time series forecasting because the excellent ability in fitting the relationship between data and cost function. However, the cost functions with non-convexity make the whole problem poor interpretability and poor robustness. In this paper, a novel hybrid supervised approach is proposed to solve the above problems. The proposed approach has adopted local convolutional neural networks (LCNNs) for convexity preserving of the cost function, in this way, a non-convex problem can be transformed as a convex problem so that heuristic optimization algorithms is adopted to find optimal parameters, and it helps to construct a more stable model. Highway Gate (HG) algorithm is adopted to decrease the computation complexity of the proposed model. The numerical simulation results indicate that the proposed method is not only effective for solving convergence problem cost by non-convexity, but also beneficial to improve accuracy and stability of the traditional ML for wind speed time series forecasting.