Achieving high resolution images is of great importance in ghost imaging. We present a super-resolution image reconstruction algorithm with sparse measurements based on the theory of compressed sensing and the prior knowledge of the point spread function of the ghost imaging system. A computational ghost imaging experimental setup with a digital mirror device is built to verify the effect of this algorithm on increasing the resolution of the ghost imaging system. In addition, we compare the result with that from the traditional ghost imaging algorithm. The experiments show that we can obtain super-resolution images by this algorithm with the sparse measurements. This approach can break through the Rayleigh limit of the imaging system and obtain super-resolution images.