The application of directional antennas in wireless ad hoc networks offers numerous benefits, such as the extended communication range, the increased spatial reuse, the improved capacity and the suppressed interference. However, directional antennas can cause new location-dependent carrier sensing problems, such as new hidden terminal and deafness problems, which can severely degrade the network performance. Recently, a few schemes have been proposed to address these problems. However, most of these existing methods can only partially solve the hidden terminal and deafness problems. Some of them even bring significant performance overhead. In this paper, we propose a novel MAC protocol, in terms of the busy-tone based directional medium access control (BT-DMAC) protocol. In BT-DMAC, when the transmission is in progress, the sender and the receiver will turn on their omni-directional busy tones to protect the on-going transmission. Integrating with the directional network allocation vector (DNAV), the scheme can almost mitigate the hidden terminal problem and the deafness problem completely. We then propose an analytical model to investigate the throughput performance of BT-DMAC. The numerical results show that BT-DMAC outperforms other existing directional MAC schemes. We next evaluate the performance of BT-DMAC through extensive simulation experiments. The results show that our proposed BT-DMAC scheme has superior performance to other existing solutions, in terms of higher throughput.