Frequent subgraph mining has been extensively studied on certain graph data. However, uncertainties are inherently accompanied with graph data in practice, and there is very few work on mining uncertain graph data. This paper investigates frequent subgraph mining on uncertain graphs under probabilistic semantics. Specifically, a measure called varphi-frequent probability is introduced to evaluate the degree of recurrence of subgraphs. Given a set of uncertain graphs and two numbers 0 varphi,tau < 1, the goal is to quickly find all subgraphs with varphi-frequent probability at least tau. Due to the NP-hardness of the problem, an approximate mining algorithm is proposed for this problem. Let 0 < delta < 1 be a parameter. The algorithm guarantees to find any frequent subgraph S with probability at least \left(\frac{1 - \delta}{2}\right)s, where s is the number of edges of S. In addition, it is thoroughly discussed how to set $\delta$ to guarantee the overall approximation quality of the algorithm. The extensive experiments on real uncertain graph data verify that the algorithm is efficient and that the mining results have very high quality.