Autonomous exploration is one of the important parts to achieve the fast autonomous mapping and target search. However, most of the existing methods are facing low-efficiency problems caused by low-quality trajectory or back-and-forth maneuvers. To improve the exploration efficiency in unknown environments, a fast autonomous exploration planner (FAEP) is proposed in this paper. Different from existing methods, we firstly design a novel frontiers exploration sequence generation method to obtain a more reasonable exploration path, which considers not only the flight-level but frontier-level factors in the asymmetric traveling salesman problem (ATSP). Then, according to the exploration sequence and the distribution of frontiers, an adaptive yaw planning method is proposed to cover more frontiers by yaw change during an exploration journey. In addition, to increase the speed and fluency of flight, a dynamic replanning strategy is also adopted. We present sufficient comparison and evaluation experiments in simulation environments. Experimental results show the proposed exploration planner has better performance in terms of flight time and flight distance compared to typical and state-of-the-art methods. Moreover, the effectiveness of the proposed method is further evaluated in real-world environments.