A graph convolutional network (GCN) has demonstrated impressive success in hand pose and shape estimation, due to its high interpretability and powerful capability for dealing with non-Euclidean data. In traditional GCN-based hand pose and shape estimation methods, the Chebyshev spectral graph convolution is most widely-used, and it is directly introduced to a simple multilayer network. In terms of the form, this graph convolution does not resemble a standard 2D convolution on an image. In terms of the practical effect, this graph convolution equally treats a center node and its neighbors. Inspired by action recognition studies, we introduce an adaptive graph convolution to hand pose and shape estimation, which not only considers the difference between a center node and its neighbors, but also considers the edge importance. Based on the adaptive graph convolution, we design a multilayer graph residual network with a double-skipconnection architecture. Extensive ablation studies are conducted to demonstrate the improvements due to the use of the adaptive graph convolution and the advantages of the graph residual network. Our method outperforms recent baselines on the public FreiHAND hand pose and shape estimation dataset.