This paper focuses on the answer sentence selection task. Unlike previous work, which only models the relation between the question and each candidate sentence, we propose Multi-Perspective Graph Encoder (MPGE) to take the relations among the candidate sentences into account and capture the relations from multiple perspectives. By utilizing MPGE as a module, we construct two answer sentence selection models which are based on traditional representation and pre-trained representation, respectively. We conduct extensive experiments on two datasets, WikiQA and SQuAD. The results show that the proposed MPGE is effective for both types of representation. Moreover, the overall performance of our proposed model surpasses the state-of-the-art on both datasets. Additionally, we further validate the robustness of our method by the adversarial examples of AddSent and AddOneSent.