In the domain of single image super-resolution, algorithms based on Gaussian process regression neither exploit the association relationships among similar patches, nor do they discriminate between these patches with similar properties to augment the volume of the training set, which leads to obvious noise and artifacts in reconstructed high-resolution images. To overcome this problem, a new super-resolution algorithm based on multi-task Gaussian process regression is proposed. This algorithm introduces the idea of multi-task learning to partition the input low-resolution image into overlapped patches and considers the super-resolution process of each patch as a task. In the process of modeling similar tasks, the parameter set obtained by optimal solving for representing the commonness and difference gives generalization ability, improves prediction accuracy improved, makes the reconstructed high-resolution image clear and sharp, and suppresses noise and artifacts significantly. A large number of experiments to process common testing images and a public image test set subjectively and objectively demonstrate that this algorithm is superior to similar state of the art algorithms, and the peak signal to noise ratio is approximately 0.5 dB higher than that of other common super-resolution algorithms.