© 2017 by the authors. Recently, various unicast routing protocols have been proposed to deliver measured data from the sensor node to the sink node within the predetermined deadline in wireless sensor networks. In parallel with their approaches, some applications demand the specific service, which is based on broadcast to all nodes within the deadline, the feasible real-time traffic model and improvements in energy efficiency. However, current protocols based on either flooding or one-to-one unicast cannot meet the above requirements entirely. Moreover, as far as the authors know, there is no study for the real-time broadcast protocol to support the application-specific traffic model in WSN yet. Based on the above analysis, in this paper, we propose a new (m, k)-firm-based Real-time Broadcast Protocol (FRBP) by constructing a broadcast tree to satisfy the (m, k)-firm, which is applicable to the real-time model in resource-constrained WSNs. The broadcast tree in FRBP is constructed by the distance-based priority scheme, whereas energy efficiency is improved by selecting as few as nodes on a tree possible. To overcome the unstable network environment, the recovery scheme invokes rapid partial tree reconstruction in order to designate another node as the parent on a tree according to the measured (m, k)-firm real-time condition and local states monitoring. Finally, simulation results are given to demonstrate the superiority of FRBP compared to the existing schemes in terms of average deadline missing ratio, average throughput and energy consumption.