Enabling machines with the capability to recognize and comprehend metaphors is a crucial step toward achieving artificial intelligence. In linguistic theories, metaphor can be identified through Metaphor Identification Procedure (MIP) or Selectional Preference Violation (SPV), both of which are typically considered as matching tasks in the field of natural language processing. However, the implementation of MIP poses a challenge due to the semantic uncertainty and ambiguity of literal meanings of words. Simultaneously, SPV often struggles to recognize conventional metaphors. Inspired by Quantum Language Model (QLM) for modeling semantic uncertainty and fine-grained feature matching, we propose a quantum-inspired matching network for metaphor detection. Specifically, we use the density matrix to explicitly characterize the literal meanings of the target word for MIP, in order to model the uncertainty and ambiguity of the literal meanings of words. This can make SPV effective even in the face of conventional metaphors. MIP and SPV are then achieved by fine-grained feature matching. The results of the experiment finally demonstrated our approach has strong competitiveness.