The distance spectral radius of a connected hypergraph is the largest eigenvalue of its distance matrix. In this paper we present a new transformation that decreases distance spectral radius. As applications , if ∆ ≥ ⌈ m+1 2 ⌉, we determine the unique k-uniform hypertree of fixed m edges and maximum degree ∆ with the minimum distance spectral radius. And we characterize the k-uniform hypertrees on m edges with the fourth, fifth, and sixth smallest distance spectral radius. In addition, we obtain the k-uniform hypertree on m edges with the third largest distance spectral radius.