To address the problems that the most of deep learning-based super-resolution reconstruction algorithms focus on learning from a large amount of external training data while ignoring the internal knowledge of an image itself and focusing too much on local features, a pyramid-like graph residual network is proposed for image super-resolution reconstruction. Firstly, the algorithm builds a residual graph convolution structure, which converts the extracted feature maps into vertices of pre-generated graph structures to constitute graph structure data by using a kind of pre-generated graph structure, so as to learn the internal topology of the features themselves by graph convolution, and the residuals are used to learn a moderate deepening graph convolution network to improve the reconstruction performance. Then, the algorithm builds a pyramid-like multi-dilated convolution structure, which avoids the defect of not completely covering all pixel points by making full use of different sizes of perceptual fields and better fuses feature information at different scales. Finally, experimental results show that the proposed algorithm significantly outperforms the mainstream super-resolution algorithms with better objective and subjective metric results.