In the realistic communication environment, due to the noise, packet conflict, signal attenuation and other factors, information exchange is generally unreliable among nodes in the wireless sensor networks. Broadcast is a widely-used operation, and building an energy-efficient broadcast algorithm has important theoretical and application value in improving the performance of wireless sensor networks. This paper studies the minimum energy broadcast problem of wireless sensor networks with the unreliable communications. Firstly, it analyzes the minimum energy consumption of communication model between adjacent nodes and presents the optimal transmission radius that can guarantee the neighbor node to receive packets with probability no less than P^*. Then, it discusses the relationship between multi-hop relay strategy and location information of nodes. It finally presents a PSO-based broadcast algorithm with minimum spanning tree, which can guarantee that all nodes in the network will receive packets with probability no less than P^* and minimize the total energy consumption. The simulation results show that the presented broadcast algorithm can not only guarantee all nodes to receive packets with probability no less than P^*, but also consume less energy and have better performance compared with the improved BIP algorithm.