Given an incomplete event chain, script learning aims to predict the missing event, which can support a series of NLP applications. Existing work cannot well represent the heterogeneous relations and capture the discontinuous event segments that are common in the event chain. To address these issues, we introduce a heterogeneous-event (HeterEvent) graph network. In particular, we employ each unique word and individual event as nodes in the graph, and explore three kinds of edges based on realistic relations (e.g., the relations of word-and-word, word-and-event, event-and-event). We also design a message passing process to realize information interactions among homo or heterogeneous nodes. And the discontinuous event segments could be explicitly modeled by finding the specific path between corresponding nodes in the graph. The experimental results on one-step and multi-step inference tasks demonstrate that our ensemble model HeterEvent[W+E] can outperform existing baselines.