Super-resolution (SR) reconstruction based on sparse representation and dictionary learning algorithm does not decompose the image at first. It reconstructs the image with its whole information based on sparse representation and dictionary learning algorithm directly. It is said that images can be decomposed into low-rank part and sparse part by low-rank matrix theory. Using different methods according to the characteristics of the different parts can be more effective to use the characteristics of the image. This paper proposes a super-resolution reconstruction method based on low-rank matrix and dictionary learning. The method obtains the low-rank part and sparse part of the original image via low-rank decomposition at first. The low-rank part retains most of the information of the image. The algorithm reconstructs the image based on dictionary learning method only for the low-rank part. The sparse part of the image reconstruction is not involved in the learning method, instead its reconstruction is based on linear interpolation method directly. Experimental results show that it can not only enhance the quality of the image reconstruction but also reduce the time of the reconstruction. Compared with existing algorithms, our method obtains better results in the visual effects, the peak signal to noise ratio and the running speed of the algorithm.