Most existing animal pose and shape estimation approaches reconstruct animal meshes with a parametric SMAL model. This is because the low-dimensional pose and shape parameters of the SMAL model makes it easier for deep networks to learn the high-dimensional animal meshes. However, the SMAL model is learned from scans of toy animals with limited pose and shape variations, and thus may not be able to represent highly varying real animals well. This may result in poor fittings of the estimated meshes to the 2D evidences, e.g. 2D keypoints or silhouettes. To mitigate this problem, we propose a coarse-to-fine approach to reconstruct 3D animal mesh from a single image. The coarse estimation stage first estimates the pose, shape and translation parameters of the SMAL model. The estimated meshes are then used as a starting point by a graph convolutional network (GCN) to predict a per-vertex deformation in the refinement stage. This combination of SMAL-based and vertex-based representations benefits from both parametric and non-parametric representations. We design our mesh refinement GCN (MRGCN) as an encoder-decoder structure with hierarchical feature representations to overcome the limited receptive field of traditional GCNs. Moreover, we observe that the global image feature used by existing animal mesh reconstruction works is unable to capture detailed shape information for mesh refinement. We thus introduce a local feature extractor to retrieve a vertex-level feature and use it together with the global feature as the input of the MRGCN. We test our approach on the StanfordExtra dataset and achieve state-of-the-art results. Furthermore, we test the generalization capacity of our approach on the Animal Pose and BADJA datasets. Our code is available at the project website.