ABSTRACT The small-sample problem that widely existed in the hyperspectral image (HSI) super-resolution task will lead to insufficient feature extraction in network training. Therefore, it is necessary to design an effective network to extract the feature of HSIs fully. In addition, existing HSI super-resolution (SR) networks usually capture multiple receptive fields by staking massive convolutions, which will inevitably produce many parameters. In this paper, we propose a novel HSI SR network based on the convolution neural network enhanced graph attention network (CEGATSR), which can fully capture different features by using a graph attention block (GAB) and a depthwise separable convolution block (DSCB). Moreover, the graph attention block can also capture different receptive fields by using relatively few layers. Specifically, we first divide the whole spectral bands into several groups and extract the features separately for each group to reduce the parameters. Second, we design a parallel feature extraction unit to extract non-local and local features by combining the graph attention block (GAB) and the depthwise separable convolution block (DSCB). The graph attention block makes full use of the non-local self-similarity strategy not only to self-learn the effective information but also to capture the multiple receptive fields by using relatively few parameters. The depthwise separable convolution block is designed to extract the local feature information with few parameters. Third, we design a spatial-channel attention block (SCAB) to capture the global spatial-spectral features and to distinguish the importance of different channels. A large number of experiments on three hyperspectral datasets show that the proposed CEGATSR performs better than the state-of-the-art SR methods. The source code is available at [Online]. Available: https://github.com/Dongyx1128/CEGATSR.