The strategy of constructing a virtual backbone (VB) to perform routing tasks is considered a mature method for addressing the broadcast storm problem in wireless sensor networks (WSNs). A WSN can be regarded as a unit disk graph (UDG), and its VBs can be regarded as connected dominating sets (CDSs) in the UDG. The smaller the VB is, the less overhead and wireless signal collision and interference there are in the process of communication via the VB. Therefore, when a VB is designed in a WSN, its size is naturally an important factor to be considered. In addition, other factors that are often ignored by researchers, such as the routing cost of the VB, should be considered. In this article, we focus on how to construct a VB with a small size and routing cost in a WSN. We propose two centralized approximation algorithms: one is an algorithm for constructing a VB with a guaranteed routing cost, called RCC-CDS, and the other is an algorithm for constructing a VB with a bounded diameter, called BD-CDS. The performance ratio (PR) of RCC-CDS is 142.758, and that of BD-CDS is 13.596. We compare these two algorithms with previous works though theoretical analysis and simulation experiments on the basis of algorithm performance. The results obtained show that our algorithms have better performance.