In fat-tree data center networks, routing a packet from its source to destination includes two phases, upstream (i.e. from source to watershed switch) and downstream (i.e. from watershed switch to destination). The throughput/non-blocking performance of networks hinges much on the effects of two phases above. In this paper, we propose a new routing algorithm called Global Round Robin (GRR) for fat-tree data center networks. In the upstream of GRR, each packet is sent to a toppest switch based on the GRR relationship between its source and toppest switches. Then the packet can arrive at a toppest switch in a single time slot without any blocking and buffering en route. In the downstream of GRR, the packet is routed to its destination using self-routing. The simulation results show that GRR provides the best delay/throughput performance among the existing routing algorithms for data center networks.