A fast sparse representation face recognition algorithm based on Gabor dictionary and SL0 norm is proposed in this paper. The Gabor filters, which could effectively extract local directional features of the image at multiple scales, are less sensitive to variations of illumination, expression and camouflage. SL0 algorithm, with the advantages of calculation speed,require fewer measurement values by continuously differentiable function approximation L0 norm and reconstructed sparse signal by minimizing the approximate L0 norm. The algorithm obtain the local feature face by extracting the Gabor face feature, reduce the dimensions by principal component analysis, fast sparse classify by the SL0 norm. Under camouflage condition, The algorithm block the Gabor facial feature and improve the speed of formation of the Gabor dictionary. The experimental results on AR face database show that the proposed algorithm can improve recognition speed and recognition rate to some extent and can generalize well to the face recognition, even with a few training image per class.