Graph structures are extensively used in many areas since they can represent complex structured data. Graph similarity search, as one of the popular graph applications, aims to find all graphs that are similar to a given query graph from a given graph database, and it has been widely applied in fields such as cheminformatics and pharmacological informatics. However, with the advent of complex graph structure, the search for complex graph structures has become unfeasible locally. There is a trend to outsource graph storage and graph search to the cloud. Outsourced computing can alleviate local pressures, but it also brings the risk of privacy information leakage, so a privacy-preserving graph similarity search system is crucial. Wang et al. in [12] implement a privacy-preserving graph similarity search system based on two cloud servers. In this paper, we propose a privacy-preserving graph similarity search system through the graph edit distance computation with the involvement of three-party cloud servers. The encryption of graph structures is achieved through the replicated secret sharing (RSS), where each cloud server holds only one part of the shares of a secret value to prevent any server from obtaining the complete secret. And the cloud servers implement the protocols to search the similar graphs according to the secure multi-party computation (MPC). Our scheme has been proven to be feasible both theoretically and experimentally.