In order to reduce the power consumption of mobile stations and the air interface resource utilization of serving base stations, IEEE802.16e introduced a sleep mode, in which a mobile station stopped its normal service. In order to balance the average energy consumption and the average waiting time, this paper proposed a power function increase algorithm for the sleep mode. According to different traffic requirements, this algorithm can adjust the increase of sleep interval with different a. Average response time and average power consumption are two performance measurements. Through numerical analysis and simulation experiments, the authors compared the above two performance measurements of different sleep mode algorithms under a＞0. Simulation results have shown that the power function increase algorithm with a=1.2 has the lowest average power consumption. It saves the average energy consumption by 11% and decreases the response time by 55%, compared with the exponential algorithm.