Although deep learning has been extensively studied and achieved remarkable performance on single image super-resolution (SISR), existing convolutional neural networks (CNN) mainly focus on broader and deeper architecture design, ignoring the detailed information of the image itself and the potential relationship between the features. Recently, several attempts have been made to address the SISR with graph representation learning. However, existing GNN-based methods learning to deal with the SISR problem are limited to the information processing of the entire image or the relationship processing between different feature images of the same layer, ignoring the interdependence between the extracted features of different layers, which is not conducive to extracting deeper hierarchical features. In this paper, we propose an interlayer feature representation based graph neural network for image super-resolution (LSGNN), which consists of a layer feature graph representation learning module and a channel spatial attention module. The layer feature graph representation learning module mainly captures the interdependence between the features of different layers, which can learn more fine-grained image detail features. In addition, we also unified a channel attention module and a spatial attention module into our model, which takes into account the channel dimension information and spatial scale information, to improve the expressive ability, and achieve high quality image details. Extensive experiments and ablation studies demonstrate the superiority of the proposed model.