According to the widely used IEEE 802.15.4, one of the most effective ways to reduce the power consumption of sensor nodes is to enable the optional sleep mode by radio shutdown. In this paper, we propose an extended Markov-based analytical model for IEEE 802.15.4 slotted carrier sense multiple access/collision avoidance (CSMA/CA) algorithm considering the newly enabled sleep mode. For taking account of the active/sleep transitions in our model, we particularly analyze the impact of duty cycle on throughput and power consumption. Moreover, some discussion based on the numerical results of the model is carried out for further understanding. It is showed that the results given by our model have an accurate match with the simulations, and the impacts of the sleep mode on IEEE 802.15.4 can be studied by the model well.