In order to reduce the power consumption of a mobile station, IEEE802.16e introduces the sleep mode, in which a mobile station stops its normal service. Network arrivals are often modeled as a Poisson process for analytic simplicity，but recent traffic Studies have shown that data packet inter-arrivals including Pareto distribution, are not exponentially distributed, but are heavy-tailed distributed, including Pareto distribution. In order to balance the average energy consumption and the average waiting time, this paper proposes a power function decrease algorithm for sleep mode based on Pareto distribution. Experiments and theoretical analysis show that the algorithm has a lower average energy consumption and shorter average waiting time than the algorithm proposed in IEEE 802.16e standard.