Recently, sparse representation has been successfully used in single image super-resolution reconstruction. Unlike the traditional single image super-resolution methods such as image interpolation, the super-resolution with sparse representation reconstructs image with one or several constant dictionaries learned from external databases. However, the contents can vary significantly across different patches in a single image, and the fixed dictionaries cannot suit for every patch. This paper presents a novel approach for single image super-resolution based on sparse representation, which uses group as the basic unit, and trains dictionary with external database and the input low-resolution image itself for each group to ensure that the dictionary is suitable for the patches in the group. Simultaneous sparse coding algorithm is used to accelerate the processing and improve the result. Extensive experiments on natural images show that our method achieves better results than some state-of-the-art algorithms in terms of both objective and human visual evaluations.