Thanks for the common use of Automatic Identification System (AIS) network has made a large number of the maritime traffic data to be available. Ships equipped with AIS automatically exchange navigational information with nearby ships and terrestrial AIS receivers to facilitate the tracking and monitoring of ships' location and movement for collision avoidance and control. Obviously, with increasing amount of maritime shipping traffic, the navigational collisions are one of the growing safety concerns in maritime traffic situation awareness. To understand the collision situations can help the maritime traffic managers to improve the safety control of maritime traffic. However, it is difficult to statistically analyze such collision due to the number of collected real cases of collisions are relatively low within a short period of time. To overcome the problem of low sample size, we discover traffic conflict from data collected by AIS network to substitute the real collision. Given a set of maritime traffic data collected from AIS network, we try to discover ships' movements that have conflict behaviors and these behaviors may bring a possible collision if they do not take any evasive action. We propose a framework of Clustering-And-Detection to automatically discover the clusters of conflict trajectory from AIS trajectory data in an unsupervised way. Based on real AIS data, the experimental results show that the proposed framework is able to effectively discover sets of trajectory with conflict situation from maritime AIS traffic data. The statistical analysis on the discovered sets of conflict trajectory is able to provide useful knowledge for maritime traffic monitoring.