By combining optical networks and wireless networks, Fiber Wireless (FiWi) networks are able to provide broadband and flexible communication. In order to reduce energy consumption of STAtions (STAs) and Optical Network Units (ONUs), there are several power saving mechanisms in optical networks and wireless networks. Generally, power saving mechanisms lead to delay. The delay problem becomes more critical in FiWi networks where multiple power saving mechanisms are used at the same time to reduce energy consumption. In this paper, we analyze the delay by considering the relationship between the power saving mechanisms, which independently control the STAs and the ONUs in FiWi networks, and point out the problem that two delays can occur at the same time. In order to address the problem, we propose a novel power saving mechanism of STAs, which controls the STAs by synchronizing two power saving mechanisms for ONUs and STAs. Through mathematical analysis and numerical evaluation, we confirm that the proposed method can significantly reduce energy consumption without any increase in latency.