Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. In this work, we propose a relational message passing method for knowledge graph completion. Different from existing embedding-based methods, relational message passing only considers edge features (i.e., relation types) without entity IDs in the knowledge graph, and passes relational messages among edges iteratively to aggregate neighborhood information. Specifically, two kinds of neighborhood topology are modeled for a given entity pair under the relational message passing framework: (1) Relational context, which captures the relation types of edges adjacent to the given entity pair; (2) Relational paths, which characterize the relative position between the given two entities in the knowledge graph. The two message passing modules are combined together for relation prediction. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that, our method PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. PathCon is also shown applicable to inductive settings where entities are not seen in training stage, and it is able to provide interpretable explanations for the predicted results. The code and all datasets are available at https://github.com/hwwang55/PathCon.