Entity summarization is a novel and efficient way to understand real-world facts and solve the increasing information overload problem in large-scale knowledge graphs (KG). Existing studies mainly rely on ranking independent entity descriptions as a list under a certain scoring standard such as importance. However, they often ignore the relatedness and even semantic overlap between individual descriptions. This may seriously interfere with the contribution judgment of descriptions for entity summarization. Actually, the entity summary is a whole to comprehensively integrate the main aspects of entity descriptions, which could be naturally treated as a set. Unfortunately, the exploration of these set characteristics for entity summarization is still an open issue with great challenges. To that end, we draw inspiration from a set completion perspective and propose an entity summarization method with complementarity and salience (ESCS) to deeply exploit description complementarity and salience in order to form a summary set for the target entity. Specifically, we first generate entity description representations with textual features in the description embedding module. For the purpose of learning complementary relationships within the entire summary set, we devise a bi-directional long short-term memory structure to capture global complementarity for each summary in the summary complementarity learning module. Meanwhile, in order to estimate the salience of individual descriptions, we calculate similarities between semantic embeddings of the target entity and its property-value pairs in the description salience learning module. Next, with a joint learning stage, we can optimize ESCS from a set completion perspective. Finally, a summary generation strategy is designed to infer the entire summary set step-by-step for the target entity. Extensive experiments on a public benchmark have clearly demonstrated the effectiveness of ESCS and revealed the potential of set completion in entity summarization task.