In most of the previous research on wireless ad hoc networks, omni-directional antennas are usually used. Smart antennas, however, may offer some benefits, i.e., enhancement of spatial reuse of the wireless channel and extension of the transmission range. This paper proposes a MAC protocol called SWAMP for ad hoc networks using smart antennas based on IEEE 802.11 DCF. SWAMP consists of dual access mode which takes advantage of the two benefits. Simulation studies show SWAMP has high throughput, low end-to-end delay and low overhead compared to the IEEE 802.11, DMAC and MMAC.