This paper presents an energy-efficient algorithm based on the connected dominating set (CDS) for a wireless sensor networks (WSN). A CDS has been widely used for a virtual backbone construction to support routing and minimize the communication overheads in a network. Our algorithm, a single-phase single initiator (SPSI), only requires a single phase to construct a CDS in a distributed manner using localized information. It generates a small CDS with low message overhead and lower energy consumption. Furthermore, it does not rely on a global positioning system (GPS) to operate and can cope with the presence of unidirectional links. Therefore, it is simple and practical to implement. The performance of our algorithm is confirmed through simulations and validated against two leading CDS algorithms. The simulation results revealed that our algorithm is effective in reducing the CDS size, message overhead and energy consumption. © 2012 IEEE.