In this study, we addressed a path planning problem of a mobile robot to construct highly accurate 3D models of an unknown environment. Most studies have focused on exploration approaches, which find the most informative viewpoint or trajectories by analyzing a volumetric map. However, the completion of a volumetric map does not necessarily describe the completion of a 3D model. A highly complicated structure sometimes cannot be represented as a volumetric model. We propose a novel exploration algorithm that considers not only a volumetric map but also reconstructed surfaces. Unlike previous approaches, we evaluate the model completeness according to the quality of the reconstructed surfaces and extract low-confidence surfaces. The surface information is used to guide the computation of the exploration path. Experimental results showed that the proposed algorithm performed better than other state-of-the-art exploration methods and especially improved the completeness and confidence of the 3D models.