Uncertain graphs are graphs where each edge is assigned with a probability of existence. In this paper, we study the problem of hop-constrained s-t simple path enumeration in large uncertain graphs. To the best of our knowledge, we are the first to study this problem in the literature. Specifically, we propose a light-weight index to prune candidate paths by adopting the concept of probability-constrained distance. An efficient enumeration algorithm is designed based on the index structure. Experiment results on real-world datasets show that our proposed methods significantly outperform the baseline methods by up to 6 times.