The sleep mode which works upon low arrival traffic is introduced in IEEE802.16e standard to reduce the power consumption of the mobile access terminal. Due to the rapid growth in the sleep interval in the exponential growth algorithm prescribed in IEEE802.16e, the power saving efficiency of the mobile access terminal is limited and the average delay time of receiving data frames is prolonged when the arrival rate of data frames is low. To obtain lower power consumption and shorter average delay time, the logarithmic growth algorithm is proposed. Theoretical analysis and simulation results show that the proposed algorithm has lower average power consumption and shorter average delay time than the exponential growth algorithm, and it can meet the requirements of low traffic and real-time applications.