In this paper, we study a Steiner tree related problem called “Terminal Steiner Tree with Bounded Edge Length”: given a set of terminal points P in a plane, one is asked to find a Steiner tree T such that any point in P is a leaf in T and the length of each edge in T is no more than a constant b. The objective of the problem is to minimize the number of Steiner points in T. This problem is motivated from wireless network design and has various applications in wireless network area. We present a constant approximation algorithm for this problem in this paper.