Partial face recognition is a problem that often arises in practical settings and applications. We propose a sparse representation-based algorithm for this problem. Our method firstly trains a dictionary and the classifier parameters in a supervised dictionary learning framework and then aligns the partially observed test image and seeks for the sparse representation with respect to the training data alternatively to obtain its label. We also analyze the performance limit of sparse representation-based classification algorithms on partial observations. Finally, face recognition experiments on the popular AR data-set are conducted to validate the effectiveness of the proposed method.