Abstract Communications in industrial applications such as wireless factory automation demand different timing requirements. Providing timely medium access of the critical traffic and its prioritization over regular traffic at the same time is a significant challenge in industrial wireless networks. Successive Interference Cancellation (SIC) technique is an effective way to decrease access delay by allowing multiple packets reception concurrently. A series of novel Medium Access Control (MAC) protocols are proposed to differentiate access delay for various traffic types or exploit SIC for unique traffic type. Our protocol in this paper (MPDMAC-SIC) is the first priority based distributed MAC protocol that employs SIC to provide low access delay and accommodate different types of traffic for multi-hop industrial wireless networks. Two major contributions of our work are: first, we propose a low delay protocol for priority based multi-hop industrial wireless networks by enabling multiple packet reception on power domain with SIC. In MPDMAC-SIC, a power contention procedure other than traditional RTS/CTS contention in CSMA/CA DCF is introduced to allocate proper transmitting power for transmitters. Second, MPDMAC-SIC is modeled by discrete time Markov chain to minimize access delay by optimizing window size in power contention. According to the simulation results, MPDMAC-SIC performs better on access delay and packet arriving rate, compared to the existing good performing priority based CSMA/CA in both single-hop and multi-hop networks.