Link prediction and node classification are two important downstream tasks of network representation learning. Existing methods have achieved acceptable results but they perform these two tasks separately, which requires a lot of duplication of work and ignores the correlations between tasks. Besides, conventional models suffer from the identical treatment of information of multiple views, thus they fail to learn robust representation for downstream tasks. To this end, we tackle link prediction and node classification problems simultaneously via multi-task multi-view learning in this paper. We first explain the feasibility and advantages of multi-task multi-view learning for these two tasks. Then we propose a novel model named as MT-MVGCN to perform link prediction and node classification tasks simultaneously. More specifically, we design a multi-view graph convolutional network to extract abundant information of multiple views in a network, which is shared by different tasks. We further apply two attention mechanisms: view attention mechanism and task attention mechanism to make views and tasks adjust the view fusion process. Moreover, view reconstruction can be introduced as an auxiliary task to boost the performance of the proposed model. Experiments on real-world network datasets demonstrate that our model is efficient yet effective, and outperforms advanced baselines in these two tasks.