Power consumption has become a key issue during the last few years and that of Internet in particular, is not negligible. With the advent of cloud computing and the exponential growth of traffic with it, power consumption has become an increasing concern for data centers. While power-aware algorithms have been investigated quite well in the wireless context, their developments in wire-line networks, especially in traffic-intensive data centers remain to be explored. In this paper, we propose a novel power-aware flow routing algorithm on the premise of performance for fat-tree data center topology and call it GreenFlow. With a maximum link utilization threshold, we route flows as centrally as possible and turn off switches without traffic flowing through them. Moreover, we take load balancing into consideration when rerouting flows on the open devices and their corresponding available paths. Verified by simulation results, our algorithm performs well in typical traffic patterns including uniform traffic, mice-elephant traffic and hotspot traffic. Earning about 20%~58% power reduction when the load is below 0.45, the performance of GreenFlow is still comparable to that of the current best-performing routing algorithms, such as CONGA and LetFlow.