Magnetic Resonance Imaging （MRI） is widely used in the diagnosis of complex diseases because of its non-invasiveness and good soft tissue contrast. Due to the low speed of MRI， most of the acceleration is currently performed by highly undersampled Magnetic Resonance （MR） signals in k-space. However， the representative algorithms often have the problem of blurred details when reconstructing highly undersampled MR images. Therefore， a highly undersampled MR image reconstruction algorithm based on Residual Graph Convolutional Neural nETwork （RGCNET） was proposed. Firstly， auto-encoding technology and Graph Convolutional neural Network （GCN） were used to build a generator. Secondly， the undersampled image was input into the feature extraction （encoder） network to extract features at the bottom layer. Thirdly， the high-level features of MR images were extracted by the GCN block. Fourthly， the initial reconstructed image was generated through the decoder network. Finally， the final high-resolution reconstructed image was obtained through a dynamic game between the generator and the discriminator. Test results on FastMRI dataset show that at 10%， 20%， 30%， 40% and 50% sampling rates， compared with spatial orthogonal attention mechanism based MRI reconstruction algorithm SOGAN（Spatial Orthogonal attention Generative Adversarial Network）， the proposed algorithm decreases 3.5%， 26.6%， 23.9%， 13.3% and 14.3% on Normalized Root Mean Square Error （NRMSE）， increases 1.2%， 8.7%， 6.9%， 2.9% and 3.2% on Peak Signal-to-Noise Ratio （PSNR） and increases 0.8%， 2.9%， 1.5%， 0.5% and 0.5% on Structural SIMilarity （SSIM） respectively. At the same time， subjective observation also proves that the proposed algorithm can preserve more details and have more realistic visual effects.