Automatic prediction on the peer-review aspect scores of academic papers can be a useful assistant tool for both reviewers and authors. To handle the small size of published datasets on the target aspect of scores, we propose a multi-task approach to leverage additional information from other aspects of scores for improving the performance of the target. Because one of the problems of building multi-task models is how to select the proper resources of auxiliary tasks and how to select the proper shared structures. We propose a multi-task shared structure encoding approach which automatically selects good shared network structures as well as good auxiliary resources. The experiments based on peer-review datasets show that our approach is effective and has better performance on the target scores than the single-task method and naive multi-task methods.