Metaphor identification is usually formulated as a sequence labeling or a syntactically related word-pair classification problem. In this paper, we propose a novel formulation of metaphor identification as a relation extraction problem. We introduce metaphorical relations, which are links between two spans, a target span and a source-related span, which are realized in sentences. Based on spans, we can use more flexible and precise text units beyond single words for capturing the properties of the target and the source. We create a dataset for Chinese metaphorical relation extraction, with more than 4,200 sentences annotated with metaphorical relations, corresponding target/source-related spans, and fine-grained span types. We develop a span-based end-to-end model for metaphorical relation extraction and demonstrate its effectiveness. We expect that metaphorical relation extraction can serve as a bridge for connecting linguistic and conceptual metaphor processing. The dataset is at https://github.com/cnunlp/CMRE.