Consider spanning trees on the two-dimensional Sierpinski gasket SG(n) where stage n is a non-negative integer. For any given vertex x of SG(n), we derive rigorously the probability distribution of the degree j ∈{1,2,3,4} at the vertex and its value in the infinite n limit. Adding up such probabilities of all the vertices divided by the number of vertices, we obtain the average probability distribution of the degree j. The corresponding limiting distribution φ_j gives the average probability that a vertex is connected by 1, 2, 3 or 4 bond(s) among all the spanning tree configurations. They are rational numbers given as φ₁=10957/40464, φ₂=6626035/13636368, φ₃=2943139/13636368, φ₄=124895/4545456.