This paper proposes a new problem of complementary evidence identification for open-domain question answering (QA). The problem aims to efficiently find a small set of passages that covers full evidence from multiple aspects as to answer a complex question. To this end, we proposes a method that learns vector representations of passages and models the sufficiency and diversity within the selected set, in addition to the relevance between the question and passages. Our experiments demonstrate that our method considers the dependence within the supporting evidence and significantly improves the accuracy of complementary evidence selection in QA domain.