Lightweight unmanned aerial vehicles (UAVs) have been widely used in image acquisition for 3D reconstruction. With the availability of compact and high-end imaging sensors, UAVs can be the platform for precise photogrammetric reconstruction. However, the completeness and precision of complex environment or targets highly rely on the flight planning due to the self-occlusion of structures. Flight paths with back-and-forth pattern and nadir views will result in incompleteness and precision loss of the 3D reconstruction. Therefore, multiple views from different directions are preferred in order to eliminate the occlusion. We propose a 3D path planning method for multirotor UAVs aiming at capturing images for complete and precise photogrammetric 3D reconstructions. This method takes the coarse model from an initial flight as prior knowledge and estimates its completeness and precision. New imaging positions are then planned taking photogrammetric constraints into account. The real-world experiment on a ship lock shows that the proposed method can acquire a more complete result with similar precision compared with an existing 3D planning method.