Fiber-Wireless (FiWi) access networks, have rapidly matured as a last mile Internet access network solution due to their novel combination of Ethernet Passive Optical Networks (EPON) as a backhaul and Wireless Mesh Networks (WMN) as an access network. The high bandwidth provided by the optical lines, as well as the flexibility offered by the wireless network, offers a great degree of cost-efficiency in terms of sharing an optical line with a number of simultaneous users. In a FiWi network, Gateways (GWs) located between the EPON and WMN serve both the function of an Optical Network Unit (ONU) in the EPON and a mesh router in WMN. Since all of the downstream from the EPON to the WMN and all of the upstream from the WMN to the EPON must be exchanged at GWs, traffic distribution technique between GWs is necessary to achieve efficient utilization of the network resources. Controlling the downstream traffic is a significant issue in preventing performance degradation due to network congestion at the GWs, because the bandwidth of WMN is generally narrower than that of the EPON. In addition, the number of hops from a GW to an end-user in the WMN needs to be taken into account in the traffic distribution process, because the increased number of hops results in lower communication efficiency due to mutual interferences between adjacent links and effects of cross traffic. Therefore, in this paper, we focus on the downstream controlling of FiWi networks, and propose a traffic distribution scheme which utilizes an aspect of EPON to properly distribute traffic load among GWs. A hop count limitation mechanism is adopted to avoid throughput degradation caused by increased wireless interference and effects of cross traffic in the WMN. Simulation results show a trade-off relationship between fair load balancing among GWs and high throughput for end-users, and the proposed scheme can accommodate it by regulating hop count limitation.