As semiconductor technology evolves, computing platforms attempt to integrate hundreds of processing cores and associated interconnects into a single chip. Network-on-chip (NoC) technology has been widely used for data exchange centers in recent years. As the core element of the NoC, the round-robin arbiter provides fair and fast arbitration, which is essential to ensure the high performance of each module on the chip. In this paper, we propose a low-latency fair switch arbiter (FSA) architecture based on the tree structure search algorithm. The FSA uses a feedback-based parallel priority update mechanism to complete the arbitration within the leaf nodes and a lock-based round-robin search algorithm to guarantee global fairness. To reduce latency, the FSA keeps the lock structure only at the leaf node so that the complexity of the critical path does not increase. Meanwhile, the FSA achieves a critical path with only O(log4N) delay by using four input nodes in parallel. The latency of the proposed circuit is on average 22.2% better than the existing fair structures and 8.1% better than the fastest arbiter, according to the synthesis results. The proposed architecture is well suited for high-speed network-on-chip switches and has better scalability for switches with large numbers of ports.