Using directional antenna in ad hoc networks, offer many benefits in contrast to their classical omni-directional counterparts. The most important benefits are the significant improvement in spatial reuse, reduction of the radio interference, increase in coverage range and subsequently an increase in network capacity on the whole. On the other hand, directional transmission increases the hidden terminal problem and the problem of deafness. To best utilize directional antennas, a suitable Medium Access Control (MAC) protocol must be designed. Current MAC protocols, such as the IEEE 802.11 standard for Wireless LANs, assume the omni-directional antenna at its Physical layer and thus do not fully exploit the capabilities of a directional antenna. In this thesis, we propose a MAC protocol for wireless ad hoc networks which fully exploits the potentials of directional antennas. The first part of our design studies the issues related to directional MAC protocols and we use this knowledge to carefully design the proposed MAC protocol for ad hoc networks using directional antennas. We evaluate our work through simulation studies performed on the network simulator — NS2. Numerical results obtained are promising and show that our protocol offers significant improvement in throughput when compared to the performance of traditional 802.11 MAC protocol and D-MAC which is a Directional MAC protocol for ad hoc networks.