Multi-head attention is appealing for its ability to jointly extract different types of information from multiple representation subspaces. Concerning the information aggregation, a common practice is to use a concatenation followed by a linear transformation, which may not fully exploit the expressiveness of multi-head attention. In this work, we propose to improve the information aggregation for multi-head attention with a more powerful routing-by-agreement algorithm. Specifically, the routing algorithm iteratively updates the proportion of how much a part (i.e. the distinct information learned from a specific subspace) should be assigned to a whole (i.e. the final output representation), based on the agreement between parts and wholes. Experimental results on linguistic probing tasks and machine translation tasks prove the superiority of the advanced information aggregation over the standard linear transformation.