In this paper, we tackle the packet scheduling problem in IEEE 802.16e wireless metropolitan area network (WMAN), where the Sleep Mode is applied to save energy of mobile stations (MSs). Our objective is to design an energy efficient scheduling policy which works closely with the sleep mode mechanism so as to maximize battery lifetime in MSs. To the best of our knowledge no power saving scheduling algorithms based on sleep mode defined in IEEE 802.16e have been proposed so far in the literature. We propose a longest virtual burst first (LVBF) scheduling algorithm which schedules packets of MSs in a virtual burst mode where there is one primary MS and multiple secondary MSs sharing the wireless link resource. LVBF prolongs MSs' lifetime by reducing the average time when MSs stay in the idle state and the number of state transitions between the awake and sleep states. Simulation results show that, in comparison with the round robin scheduling scheme, LVBF can produce significant overall energy saving, while guaranteeing the QoS requirements of MSs in terms of their minimum data rates.