A Fat-Tree topology has multiple paths between any pair of hosts. The delay for the multiple paths with an equal number of hops depends mainly on the queuing delay. However, most of the existing load-balancing schemes do not sufficiently exploit the characteristics of Fat-Tree. In most schemes load-balancing is performed at a flow level. Packet-level load-balancing schemes usually require the availability of special transport layer protocols to address packet reordering. In this paper, we propose a new packet-level load-balancing scheme which can enhance network utilization while minimizing packet reordering in Fat-Trees. Simulation results show that the proposed scheme provides as high TCP throughput as a randomized flow-level Valiant load balancing scheme for a best case.