Growing energy demands in the information and communication technology (ICT) sector have been recognized as a major challenge worldwide. Researchers have been actively working to address this challenge, and the major focus centers around improving the energy efficiency of access networks, which are known for consuming about three-quarters of the total network power. Among various access networks, the hybrid wireless-optical broadband access network (WOBAN), which combines a passive optical network (PON) with broadband wireless technology, is highly regarded for its enormous capacity, cost efficiency, and ease of deployment. To develop a green WOBAN, it is important to focus on reducing its power consumption, and in this work, we present an efficient resource management technique for WOBAN that reduces the power consumption of the optical line terminal (OLT) and optical network unit (ONU) by introducing sleep modes for the OLT and ONU, based on the service class and traffic load. Moreover, it considers the quality-of-service requirement of each service class. Simulation results confirm that our proposed solution can save a significant amount of power in the WOBAN network without sacrificing the quality of service of end applications.