For the medium access control (MAC) protocol of mobile ad hoc networks, several power saving mechanisms, including that of IEEE 802.11, have been presented to reduce power consumption as much as possible. They usually focused on shortening the duration of the awake state. We observed that longer sleeping period may result in seriously long delivery latency and the consequent unnecessary power consumption as well, because the packets can go forward only one hop for a fixed interval. In this paper, we propose Fast Flooding in Power Save Mode (FFPSM), a modification of IEEE 802.11 power save mode operation, which allows the flooding packets to be forwarded several hops in one transmission period. FFPSM does not reduce the compulsory awake period, but maximizes its utilization. Each node propagates the announcements of next flooding to nodes of several hops away, thus the packets can travel multiple hops during one interval. Simulation results show that the proposed approach significantly reduces the end-to-end delay without consuming more energy.