Currently, convolution neural network is widely applied in image compression frameworks. However, classical convolution can only capture local information because of the heavy restriction of the fixed-shape receptive field. In this paper, we propose a novel image compression network, which introduces graph convolution block (GCB) to enhance the capability of extracting image information in the encoder. In GCB, the graph convolution and residual block are utilized to acquire local and global image features at the same time. Furthermore, an effective dequantization strategy is developed so that the decoder can learn better parameters to reconstruct more image information that is lost in quantization. Extensive experiments demonstrate that our model has outstanding performance, which outperforms existing excellent classical and learned image compression frameworks.