We present a quantum algorithm for sampling random spanning trees from a weighted graph in (\widetilde{O}(\sqrt{mn})) time, where (n) and (m) denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for dense graphs and achieves a quantum speedup over the best-known classical algorithm, which runs in (\widetilde{O}(m)) time. The approach carefully combines, on one hand, a classical method based on ``large-step’’ random walks for reduced mixing time and, on the other hand, quantum algorithmic techniques, including quantum graph sparsification and a sampling-without-replacement variant of Hamoudi’s multiple-state preparation. We also establish a matching lower bound, proving the optimality of our algorithm up to polylogarithmic factors. These results highlight the potential of quantum computing in accelerating fundamental graph sampling problems.