In wireless sensor networks, virtual backbone construction based on connected dominating set is a competitive issue for routing efficiency and topology control. Assume that a sensor networks is defined as a connected unit disk graph (UDG). The problem is to find a minimum connected dominating set of given UDG with minimum routing cost for each node pair. We present a constant approximation scheme which produces a connected dominating set D, whose size D is within a factor α from that of the minimum connected dominating set and each node pair exists a routing path with all intermediate nodes in D and with length at most 5 · d(u,v), where d(u,v) is the length of shortest path of this node pair. A distributed algorithm is also provided with analogical performance. Extensive simulation shows that our distributed algorithm achieves significantly than the latest solution in research direction.