Attributed graph clustering is challenging as it needs to effectively combine both graph structure and node feature information to accomplish node clustering. Recent studies mostly adopt graph neural networks to learn node embeddings, then apply traditional clustering methods to obtain clusters. However, their node embeddings are not specifically designed for clustering. Moreover, most of their loss functions only rely on either structure or feature information, making both kinds of information not fully retained in node embeddings. In this paper, we propose a multi-task embedding learning method (MTEL) for attributed graph clustering, which constructs two prediction tasks in terms of structure and feature based adjacency matrices respectively. To make the node embeddings helpful for the downstream clustering, in each task, we predict the minimum hop number between each pair of nodes in the adjacency matrix, so that the correlation degrees among nodes can be encoded into node embeddings. To improve the performance of the prediction task, we regularize the model parameters in these two tasks via ℓ2,1 norm, through which the model parameters can be jointly learned. Experiments on real attributed graphs show that MTEL is superior for attributed graph clustering over state-of-the-art methods.