In recent years there is a growing interest in the study of sparse representation for signals. This article extends this research into a novel model for object classification tasks. In this model, we first apply the non-negative K-SVD algorithm to learning the discriminative dictionaries using very few training samples and then represent a test image as a linear combination of atoms from these learned dictionaries based on the non-negative variation of Basis Pursuit (BP). Finally, we achieve the classification purpose by analyzing the sparse weighting coefficients. Our strategy of classification is very simple and does not ask much for the training samples. Our model is tested on two benchmark data sets Caltech-101 and UIUC-car. In both datasets, Our approach achieves the comparable performance. The idea in this paper strengthens the case for using this model in computer vision further.