Abstract: This paper focuses on the shortest distance problem in uncertain graphs, which we call expected shortest distance problem. We analyze the complexity of this problem and prove that there is no polynomial time algorithm for it. To solve this problem, we utilize random sampling methods to acquire some possible worlds of the uncertain graph, then compute the shortest distance on each and estimate expected shortest distance with the average value of the finite ones. To improve efficiency, we propose two pruning techniques, which allow us to terminate a random sampling process faster. Furthermore, considering that different sampling orders of edges do not influence the result of sampling, but will determine the number of edges to be sampled in a sampling process, we propose two sampling orders for edges to reduce the number of edges sampled in each random sampling process. Then, we propose an approximation algorithm based on random sampling using antithetic variables which is an unbiased estimator for expected shortest distance and prove that it outperforms direct random sampling in both efficiency and sampling variance, while the latter one is the key criteria for evaluating the quality of an unbiased estimator. Our experiments on real uncertain graphs of proteinprotein networks demonstrate the efficiency and accuracy of our algorithm.