Recently, sparse representation-based classification (SRC), which assigns a test sample to the class with minimum representation error via a sparse linear combination of all the training samples, has successfully been applied to hyperspectral imagery. Alternatively, spatial information, which means the adjacent pixels belong to the same class with a high probability, is a valuable complement to the spectral information. In this paper, we have presented a new spectralspatial-combined SRC method, abbreviated as SSSRC or S3RC, to jointly consider the spectral and spatial neighborhood information of each pixel to explore the spectral and spatial coherence by the SRC method. Furthermore, a fast interference-cancelation operation is adopted to accelerate the classification procedure of S3RC, named FS3RC. Experimental results have shown that both the proposed SRC-based approaches, S3RC and FS3RC, could achieve better performance than the other state-of-the-art methods.