Kernel sparse representation based classification (KSRC) in compressive sensing (CS) represents one of the most interesting research areas in pattern recognition, image processing and especially facer recognition and identification. First, it applies dimensionality reduction method to reduce data dimensionality in kernel space and then employs the L1 -norm minimization to reconstructing sparse signal. Nevertheless, these classifiers suffer from some shortcomings. KSRC is greedy in time to achieve an approximate solution of sparse representation based on L1 -norm minimization. In this paper, a new method is mathematically developed and applied for face recognition based on Gabor-wavelets for feature extraction and KSRC for precise classification. The aim of the proposed algorithm is to improve the computational efficiency of KSRC by applying a supervised kernel locality preserving projections (SKLPP) for dimension reduction. In fact, the L1 -norm minimization is performed by the use of the fast compressive sampling matching pursuit method (FCoSaMP). Experimental results prove that the proposed classification method is efficient, fast, and robust against variations of illumination, expression, and pose. Indeed, its computation time is highly reduced compared to the baseline performances.