A practical approach for the probabilistic short-term generation forecast of a wind farm is proposed in this paper. Compared with deterministic wind generation forecast, probabilistic wind generation forecast can provide important wind generation distribution information for operation, trading, and some other applications. The proposed approach is based on a sparse Bayesian learning (SBL) algorithm, which produces probabilistic forecast results by estimating the probabilistic density of the weights of Gaussian kernel functions. Furthermore, since the wind generation time series exhibits strong nonstationary property, a componential forecast strategy is used to improve the forecast accuracy. According to the strategy, the wind generation series is decomposed into several more predictable series by discrete wavelet transform, and then, the resulted series are forecasted using the SBL algorithm. To fulfill multilook-ahead wind generation forecast, a multi-SBL forecast model is constructed in the context. Tests on a 74-MW wind farm located in southwest Oklahoma demonstrate the effectiveness of the proposed approach.