A k-tree is a tree with maximum degree at most k.In this paper,we give a sharp degree sum condition for a graph to have a spanning k-tree in which specified vertices have degree less than t,where 1 ≤ t ≤ k.We denote by σk(G) the minimum value of the degree sum of k independent vertices in a graph G.Let k ≥ 2,s ≥ 0 and 1 ≤ t ≤ k be integers,and suppose G is an (s + 1)-connected graph with σk(G) ≥ |G| + (k-t)s-1.Then for any s specified vertices,G contains a spanning k-tree in which every specified vertex has degree at most t.This improves a result obtained by Matsuda and Matsumura.