A Gaussian process regression (GPR) with active learning is proposed for developing the solar irradiance point andinterval forecasting models, which consider the spatial-temporal information collected from a targeted site and a number ofneighbouring sites. To enhance the performance of the GPR-based model an active learning process is developed forconstructing an ad-hoc input feature set, selecting training data points, and optimising hyper-parameters of GPR models. Tovalidate the advantages of the proposed method, a comprehensive computational study is conducted based on solar irradiancedata collected from the northwest California area. In the point forecasting, the proposed method beats the state-of-the-artbenchmarking methods including classical statistical models and data-driven models according to values of the normalised rootmean squared error, normalised mean absolute error, normalised mean bias error, and coefficient of determination. In theinterval forecasting, the proposed method outperforms the persistence model, autoregressive model with exogenous inputs,generic GPR, as well as two recently reported forecasting methods, the bootstrap-based extreme learning machine and quantileregression, in terms of the forecasting reliability. Computational results show that the proposed method is more effective thanwell-known existing benchmarks in the point and interval forecasting of the solar irradiance.