The eavesdropping security of wireless ad hoc networks has attracted considerable attention recently. However, most of current studies only consider OMN networks, where each node is mounted with a single omni-directional antenna, which radiates radio signals in all directions and consequently leads to the high eavesdropping possibility. Compared with an omnidirectional antenna, a directional antenna can concentrate the radio signals on some desired directions so that it can potentially reduce the eavesdropping possibility. This paper investigates the eavesdropping security of wireless ad hoc networks equipped with directional antennas. In particular, we study the eavesdropping possibility of OMN networks, SDA networks in which each node is equipped with a simplistic directional antenna and RDA networks in which each node is equipped with a realistic directional antenna. More specifically, we identify the eavesdropping activity in wireless networks and propose an eavesdropping model to measure the eavesdropping possibility. We conduct extensive simulations to evaluate the eavesdropping possibility of OMN networks, SDA networks and RDA networks with considering various environment factors, such as path loss attenuation and shadowing effects. Our simulation results show that using a simplistic directional antenna or a realistic antenna in wireless networks can reduce the eavesdropping possibility.