In this paper, we propose a novel algorithm for planning exploration paths to generate 3D models of unknown environments by using a micro-aerial vehicle (MAV). Our algorithm initially determines a next-best-view (NBV) that maximizes information gain and plans a collision-free path to reach the NBV. Along the path, the MAV explores the greatest unknown area although it sometimes misses minor unreconstructed region, such as a hole or a sparse surface. To cover such a region, we propose an online inspection algorithm that consistently provides an optimal coverage path toward the NBV in real time. The algorithm iteratively refines an inspection path according to the acquired information until the modeling of a specific local area is complete. We evaluated the proposed algorithm by comparing it with other state-of-the-art approaches through simulated experiments. The results show that our algorithm outperforms the other approaches in both exploration and 3D modeling scenarios.