To solve the problems that group effect is neglected when selecting dictionary bases in sparse coding models, and distance between a features and a dictionary base can not be effectively measured by Euclidean distance, Non-negative Local Sparse Coding algorithm based on Elastic net and Histogram intersection (EH-NLSC) was proposed. Firstly, with elastic-net model introduced in the optimization function to remove the restriction on selected number of dictionary bases, multiple groups of correlation features were selected and redundant features were eliminated, improving the discriminability and effectiveness of the coding. Then, histogram intersection was introduced in the locality constraint of the coding, and the distance between the feature and the dictionary base was redefined to ensure that similar features share their local bases. Finally, multi-class linear Support Vector Machine (SVM) was adopted to realize image classification. The experimental results on four public datasets show that compared with LLC (Locality-constrained Linear Coding for image classification) and NENSC (Non-negative Elastic Net Sparse Coding), the classification accuracy of EH-NLSC is increased by 10 percentage points and 9 percentage points respectively on average, proving its effectiveness in image representation and classification.