From the perspective of media protocol control and routing of directional wireless ad hoc sensors networks, neighbor discovery protocol is an important problem to be solved first. In the past period of time, some methods have been studied on neighbor discovery protocol, but they have a common defect of link collision. The collision is caused by mutual interference of multiple transmitting nodes which are in one reception beam of the receiving node. To solve this problem, we propose a neighbor discovery algorithm using a bi-directional carrier sense collision avoidance and multi subchannels based on a scan-based algorithm (BD-SBA). Based on a scan-based algorithm (SBA), bi-directional carrier sense of the BD-SBA algorithm is performed in the first broadcast step which can reduce the collision of broadcasting the scanning request (SREQ) frames. In the second step (the reply step), the mechanism of multiple subchannels and multiple slots is applied to reduce the collision of the scanning response (SRES) frames. From the analysis and simulation, we can see that nodes using proposed algorithm can discover their neighbor nodes in fewer time. Moreover, the proposed algorithm has better performance for different beamwidths and densely distributed scenes. So it has great significance in engineering application.