To resolve the performance bottlenecks of power consumption and bandwidth shortage in data center networks (DCNs) using the traditional Electronic Packet Switching (EPS), Optical Circuit Switching (OCS) technology has gained extensive attention in recent years and showed great promises for the development of next-generation data centers capable of supporting escalating network traffic. In this context, coflow scheduling emerges as a pivotal technique for enhancing data transmission efficiency in DCNs. Nonetheless, the intrinsic constraints of OCS networks, such as port limitations and reconfiguration delays, introduce novel challenges to coflow scheduling. There are two optical path reconfiguration modes in OCS: All-Stop in which reconfiguration of a path will block the communications of all paths, and Not-All-Stop in which only the path under reconfiguration is blocked. Most of the existing studies focus on coflow scheduling in All-Stop mode, and little has been done for online scenarios in Not-All-Stop mode. This study delves into the online multi-coflow scheduling problem within DCNs supported by Not-All-Stop mode OCS, aiming to minimize the average Coflow Completion Time (CCT). We introduce an effective online algorithm comprising two main components: a coflow inter-scheduling priority strategy that takes full consideration of Not-All-Stop mode’s characteristics and network fairness, and a coflow intra-scheduling greedy algorithm (R-Greedy) that focuses on maximizing network resource utilization to determine the specific scheduling plans. The effectiveness of our algorithm is demonstrated through extensive simulation experiments.