This paper presents a novel vision-based obstacle avoidance system for flying robots working in dynamic environments. Instead of fusing multiple sensors to enlarge the view field, we introduce a bio-inspired solution that utilizes a stereo camera with independent rotational DOF to sense the obstacles actively. In particular, the rotation is planned heuristically by multiple objectives that can benefit flight safety, including tracking dynamic obstacles, observing the heading direction, and exploring the previously unseen area. With this sensing result, a flight path is planned based on real-time sampling and collision checking in state space, which constitutes an active sense and avoid (ASAA) system. Experiments demonstrate that this system is capable of handling environments with dynamic obstacles and abrupt changes in goal direction. Since only one stereo camera is utilized, this system provides a low-cost but effective approach to overcome the view field limitation in visual navigation.