Let S(m,d,k) be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k) be the k-uniform supertree obtained from a loose path u1,e1,u2,e2,…,ud,ed,ud+1 with length d by attaching m-d edges at vertex u[d/2」+1.In this paper,we mainly determine S1 (m,d,k) with the largest signless Laplacian spectral radius in S(m,d,k) for 3 ≤ d ≤ m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique k-uniform supertree with the largest signless Laplacian spectral radius among all k-uniform supertrees with n vertices and pendent edges (vertices).