Abstract: The IEEE 802.16j standard introduces Relay Station（RS） based on the IEEE 802.16d/e standard.RS sleep mode is essential for power saving，especially power constrained RS like client owned RS，nomadic RS or mobile RS，which relies on battery or solar power.It is both necessary and useful to research on IEEE 802.16j RS sleep mode.In this paper，the RS sleep mode in IEEE 802.16j is studied，and the system models for the energy consumption and the average frame delay affected by RS sleep mode are built using statistics.The influence of parameters on average energy consumption and average frame delay is analyzed at last of the paper.