Hyperspectral image (HSI) analysis is attracting a growing interest in real-world applications, many of which can finally be transformed into classification tasks. Traditional spectral-spatial HSI classification methods take advantage of the identical spatial information that is available everywhere, but this is not always the case, especially in the class boundary. A method for HSI classification based on the spectral information and the adaptive spatial context is proposed. First, we introduce a high-dimensional steering kernel to describe the adaptive spatial context and select the spatial correlative pixels of a given test pixel according to the adaptive spatial context. The selected pixels can be simultaneously sparse represented by linear combinations of a few common training samples. Then, a classifier imposing the adaptive spatial context to determine the final label of the test pixel is proposed. Experimental results on real HSIs show that our algorithm outperforms other state-of-art algorithms.