In order to improve adaptability of a class of under-actuated AUVs in unknown obstacles environment, this paper proposes a new obstacle avoidance method including three main parts. Firstly we design five basic obstacle avoidance behaviors in which emergency-yaw and holding-distance behaviors, and emergency-ascend and holding-altitude behaviors are responsible for avoiding obstacles in horizontal plane and in vertical plane respectively. All the behaviors have their own objectives and are implemented by fuzzy controllers. In the second part we present finite state automata (FSA) which are used to select a suitable obstacle avoidance behavior when an obstacle is detected. Each discrete state corresponds to a basic obstacle avoidance behavior. A set of events, oriented from changes of external environment, drive the obstacle avoidance automata from one state to another. The obstacle avoidance automata are able to make instantaneous response to external stimulation, but may come to a deadlock under some special conditions because of no considering historical information. So a supervisor based on event feedback is presented in the third part. It provides the obstacle avoidance automata with a control mode and can lead it to break a deadlock through local path planning. At last the availability and feasibility of the proposed method are demonstrated by simulation tests under more than 30 types of obstacle scenarios on an AUV semi-physical simulation platform.