Graph convolutional networks (GCN) have achieved promising performance in attributed graph clustering and semi-supervised node classification because it is capable of modeling complex graphical structure, and jointly learning both features and relations of nodes. Inspired by the success of unsupervised learning in the training of deep models, we wonder whether graph-based unsupervised learning can collaboratively boost the performance of semi-supervised learning. In this paper, we propose a multi-task graph learning model, called collaborative graph convolutional networks (CGCN). CGCN is composed of an attributed graph clustering network and a semi-supervised node classification network. As Gaussian mixture models can effectively discover the inherent complex data distributions, a new end to end attributed graph clustering network is designed by combining variational graph auto-encoder with Gaussian mixture models (GMM-VGAE) rather than the classic k-means. If the pseudo-label of an unlabeled sample assigned by GMM-VGAE is consistent with the prediction of the semi-supervised GCN, it is selected to further boost the performance of semi-supervised learning with the help of the pseudo-labels. Extensive experiments on benchmark graph datasets validate the superiority of our proposed GMM-VGAE compared with the state-of-the-art attributed graph clustering networks. The performance of node classification is greatly improved by our proposed CGCN, which verifies graph-based unsupervised learning can be well exploited to enhance the performance of semi-supervised learning.