With the large-scale deployment of emerging applications such as cloud computing microservice architecture and real-time data analytics, flow scheduling has become a key technology to improve the transmission performance of data center networks. Furthermore, the transmission control protocol on the host side typically employs a retransmission timeout (RTO) threshold to achieve data transmission reliability. However, a small threshold readily triggers unnecessary fast retransmissions for low-priority packets while a large threshold results in low-priority packets being blocked for a long time, failing to be well adapted in high-speed data center network environments. To this end, we propose a timeout-less flow scheduling mechanism called TFS to avoid unnecessary timeout retransmission and minimize the flow completion time. The basic idea behind TFS is that the switches adopt multiple priority queues to buffer different types of flows, preventing urgent flows from being blocked by non-urgent flows. Moreover, the switch periodically inspects the packet at the head of the queue in the low-priority queue. Once it is detected that packets in the low-priority queue are blocked for too long and there is a risk of timeout retransmission, the switch employs the timeout-less flow scheduling mechanism to prioritize the forwarding of packets in blocked flows, avoiding timeout retransmissions while ensuring that these packets arrive at the receiver in order. Through in-depth analysis and a series of large-scale experimental verification, we demonstrate that TFS reduces the flow completion time by up to 65% compared with the state-of-the-art flow scheduling mechanisms.