Intermittent Periodic Transmit (IPT forwarding) is known as a packet forwarding scheme that achieves highly efficient packet relays in wireless multihop networks. In the method, a source node sends source packets intermittently and periodically with some transmit period, by which co-transmission space of forwarding packets, that is defined as space between multihop nodes in packet transmission, can be controlled in accordance with the given transmit period. If the transmit period is greater than a certain limit, packet collisions due to interference are eliminated and thus packet forwarding is maximized in its efficiency. In order to compensate for broadband traffic, improvement of relay efficiency is highly expected. To this end, we consider an application of directional antenna to wireless multihop networks enabled by IPT forwarding for further improvement of relay efficiency. Upon addressing a key issue caused by the application of directional antenna, we propose a new directional MAC protocol which consists of an IPT forwarding based packet forwarding and a routing. Simulation results ensure that the proposed directional MAC achieves higher throughput and lower packet loss rate compared with a conventional packet forwarding with omni-directional antennas.