Broadcasting is a common and basic operation used to support various network protocols in wireless networks. To achieve energy-efficient broadcasting is especially important for ad hoc wireless sensor networks because sensors are generally powered by batteries with limited lifetimes. Energy consumption for broadcast operations can be reduced by minimizing the number of relay nodes based on the observation that data transmission processes consume more energy than data reception processes in the sensor nodes, and how to improve the network lifetime is always an interesting issue in sensor network research. The minimum-energy broadcast problem is then equivalent to the problem of finding the minimum Connected Dominating Set (CDS) for a connected graph that is proved NP-complete. In this paper, we introduce an Efficient Minimum CDS algorithm (EMCDS) with help of a proposed ordered sequence list. EMCDS does not concern itself with node energy and broadcast operations might fail if relay nodes are out of energy. Next we have proposed a Minimum Energy-consumption Broadcast Scheme (MEBS) with a modified version of EMCDS, and aimed at providing an efficient scheduling scheme with maximized network lifetime. The simulation results show that the proposed EMCDS algorithm can find smaller CDS compared with related works, and the MEBS can help to increase the network lifetime by efficiently balancing energy among nodes in the networks.