Many studies have been conducted on similarity join over certain (deterministic) graphs. However, in reality, graphs are often uncertain due to various factors. This paper studies similarity join on uncertain graph databases. The study employs the joint probability distribution to describe the uncertainty of edges in the graph, combines a new measure to evaluate graph similarity, and gives the formal definition of the similarity join on uncertain graph database. The paper also designs a group of filtering strategies to reduce the candidate pairs in the similarity join. A large number of experimental data show that, the method proposed in the paper is feasible and accurate.