Multi-source global broadcast is a fundamental problem in multi-hop wireless networks. The Static Multi-source Global Broadcast problem (SMGB), which considers static packet injection at all source nodes, has been extensively studied in recent years. However, packets are more likely to be continuously injected over time in realistic multi-hop wireless networks. In this paper, we focus on studying the Dynamic Multi-source Global Broadcast problem (DMGB), in which packets are continuously injected to $k$ ( $k\geq 2$ ) source nodes in the network according to a widely-used dynamic packet injection model and the objective is to disseminate each injected packet across the whole network quickly. We solve this DMGB problem under the Signal-to-Interference-plus-Noise-Ratio (SINR) interference model. Specifically, we first present a distributed randomized algorithm for solving the SMGB problem. We then iterate this SMGB algorithm repeatedly to construct a distributed DMGB algorithm. We prove the proposed DMGB algorithm is stable, i.e., the expected number of packets in each node’s message queue is bounded at any time and further the expected global broadcast latency for each injected packet is bounded. Simulation results validate the effectiveness of the proposed DMGB algorithm.