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