This paper presents a perception-aware path planner for active SLAM in dynamic environments using micro-aerial vehicles (MAV). The “Next-Best-View” planner (NBVP planner) is combined with an active loop closing, which is called the Active Loop Closing Planner (ALCP planner). The planner is proposed to avoid both static and dynamic obstacles in unknown environments while reducing the uncertainty of the SLAM system and further improving the accuracy of localization. First, the receding horizon strategy is adopted to find the next waypoint. The cost function that combines the exploration gain and the loop closing gain is designed. The former can reduce the mapping uncertainty, while the latter takes the loop closing possibility into consideration. Second, a key waypoint selection strategy is designed. The selected key waypoints, instead of all waypoints, are treated as potential loop-closing points to make the algorithm more efficient. Moreover, a fuzzy RRT-based dynamic obstacle avoidance algorithm is adopted to realize obstacle avoidance in dynamic environments. Simulations in different challenging scenarios are conducted to verify the effectiveness of the proposed algorithm.