Source　code　summaries　are　short　natural　language　descriptions　of　code　snippets　that　help　developers　better　understand　and　maintain　source　code.　There　has　been　a　surge　of　work　on　automatic　code　summarization　to　reduce　the　burden　of　writing　summaries　manually.　However,　contemporary　approaches　only　leverage　the　information　within　the　boundary　of　the　method　being　summarized　(i.e.,　local　context),　and　ignore　the　broader　context　that　could　assist　with　code　summarization.　This　paper　explores　two　global　contexts,　namely　intra-class　and　inter-class　contexts,　and　proposes　CoCoSUM:　Context-Aware　Code　Summarization　with　Multi-Relational　Graph　Neural　Network.　CoCoSUM　first　incorporates　class　names　as　the　intra-class　context　to　generate　the　class　semantic　embeddings.　Then,　relevant　Unified　Modeling　Language　(UML)　class　diagrams　are　extracted　as　inter-class　context　and　are　encoded　into　the　class　relational　embeddings　using　a　novel　Multi-Relational　Graph　Neural　Network　(MRGNN).　Class　semantic　embeddings　and　class　relational　embeddings,　together　with　the　outputs　from　code　token　encoder　and　AST　encoder,　are　passed　to　a　decoder　armed　with　a　two-level　attention　mechanism　to　generate　high-quality,　context-aware　code　summaries.　Experimental　results　show　that　CoCoSUM　outperforms　state-of-the-art　methods　and　the　global　contexts　adopted　in　CoCoSUM　can　also　strengthen　existing　code　summarization　models.　Our　replication　package　is　anonymously　available　at　https://github.com/DeepSoftwareAnalytics/cocosum.