As the IEEE 802.16e Wireless Metropolitan Access Network (WMAN) supports the mobility of a mobile station (MS), increasing MS power efficiency has become an important issue. In this paper, we analyze the sleep-mode operation for an efficient power saving mechanism for delay-guaranteed services in the IEEE 802.16e WMAN and observe the effects of the operating parameters related to this operation. For the analysis we use the M/GI/1/K queueing system with multiple vacations, exhaustive services and setup times. In the analysis, we consider the power consumption during the wake-mode period as well as the sleep-mode period. As a performance measure for the power consumption, we propose the power consumption per unit time per effective arrival which considers the power consumption and the packet blocking probability simultaneously. In addition, since we consider delay-guaranteed services, the average packet response delay is also considered as a performance measure. Based on the performance measures, we obtain the optimal sleep-mode operation which minimizes the power consumption per unit time per effective arrival with a given delay requirement. Numerical studies are also provided to investigate the system performance and to show how to achieve our objective.