In industrial wireless sensor networks (IWSNs), monitoring data generated by field devices (FDs) are supposed to be delivered to the gateway timely and reliably. The previous researches focus on the convergecast problem based on the global available channel set, where unreliable channels are blacklisted. However, in practical industrial environment, different links may have different local available channel sets (LACSs) due to the location-dependent characteristics of wireless channels. In this paper, we study the LACSs-based convergecast scheduling problem in the IWSNs with tree topologies. First, we formulate the convergecast scheduling problem in a mathematically precise form of integer programming. Then, we propose a novel method to calculate priorities for each FD, and design two effective heuristic rules of allocating channels to FDs to maximize the number of concurrent transmissions in each time slot, considering the priority of each FD and the constraints in the integer programming formulation. Finally, inspired by the proposed heuristic rules, we propose an LACSs-based convergecast scheduling (LCS) algorithms to generate efficient schedules for IWSNs in polynomial time. The simulation results show that the proposed algorithm outperforms existing works in terms of latency for different scenarios. © 2019 IEEE.