We study centralized radio access network (C-RAN) with multi-cell scheduling algorithms to overcome the challenges for supporting ultra-reliable low-latency communications (URLLC) in the fifth-generation new radio (5G NR) networks. Low-complexity multi-cell scheduling algorithms are proposed for enhancing the URLLC performance. In comparison with the conventional distributed scheduling, we show that the C-RAN architecture can significantly reduce undesirable queuing delay of URLLC traffic. The gain of user scheduling with different metrics and the benefit of packet segmentation are analyzed. The performance of the proposed solutions is evaluated with an advanced 5G NR compliant system-level simulator with high degree of realism. The results show that the centralized multi-cell scheduling achieves up to 60% latency improvement over the traditional distributed scheduling while fulfilling the challenging reliability of URLLC. It is shown that segmentation brings additional performance gain for both centralized and distributed scheduling. The results also highlight the significant impact of channel- and delay-aware scheduling of URLLC payloads.