Wind power generation rapidly grows worldwide with declining costs and the pursuit of decarbonised energy systems. However, the utilization of wind energy remains challenging due to its strong stochastic nature. Accurate wind power forecasting is one of the effective ways to address this problem. Meteorological data are generally regarded as critical inputs for wind power forecasting. However, the direct use of numerical weather prediction in forecasting may not provide a high degree of accuracy due to unavoidable uncertainties, particularly for areas with complex topography. This study proposes a hybrid short-term wind power forecasting method, which integrates the corrected numerical weather prediction and spatial correlation into a Gaussian process. First, the Gaussian process model is built using the optimal combination of different kernel functions. Then, a correction model for the wind speed is designed by using an automatic relevance determination algorithm to correct the errors in the primary numerical weather prediction. Moreover, the spatial correlation of wind speed series between neighbouring wind farms is extracted to complement the input data. Finally, the modified numerical weather prediction and spatial correlation are incorporated into the hybrid model to enable reliable forecasting. The actual data in East China are used to demonstrate its performance. In comparison with the basic Gaussian process, in different seasons, the forecasting accuracy is improved by 7.02%–29.7% by using additional corrected numerical weather prediction, by 0.65–10.23% after integrating with the spatial correlation, and by 10.88–37.49% through using the proposed hybrid method.