We propose the asynchronous receiver-initiated MAC protocol with the stair-like sleep that each node reduces its own sleep time by the sleep-change-rate depending on the number of hops from the source to the sink in wireless sensor networks (WSNs). Using the stair-like sleep, our protocol achieves the high delivery ratio, the low packet delay, and the high energy efficiency due to the reduction of the idle listening time. Our protocol can formulate the upper bound of the idle listening time because of the feature that the sleep time decreases in the geometric progression, and the reduction of the idle listening time is obtained by using the stair-like sleep. In our proposed scheme, the sink calculates the sleep change rate based on the number of hops from the source to the sink. By using the control packets which have the role of ACK, our proposed protocol can achieve the stair-like sleep by no additional control packets. In addition, even in the network condition that multi-targets are detected, and hops to the sink are changed frequently, our proposed protocol can change the sleep change rate adaptively because the sink can always obtain the number of hops from the source to the sink. Simulation results show that the proposed protocol can improve the performances in the packet delivery ratio, the packet delay, and the energy efficiency compared to the conventional receiver-initiated MAC (RI-MAC) protocol.