Image-based refined 3D reconstruction relies on high-resolution and multi-angle images of scenes. The assistance of multi-rotor drones and gimbal provides great convenience for image acquisition. However, capturing images with manual control generally takes a long time. It could easily lead to redundant or insufficient local area coverage, resulting in poor quality of the reconstructed model. We propose a surface geometric primitive-guided UAV path planning method (SGP-G) that aims to automatically and quickly plan a collision-free path to capture fewer images, based on which high-quality models can be obtained. The geometric primitives are extracted by plane segmentation on the proxy, which performs three main functions. First, a more representative evaluation of the reconstructability of the whole scene is realized. Second, two optimization strategies for different geometric primitives are executed to quickly generate a near-global optimized set of viewpoints. Third, regularly arranged viewpoints are generated to improve the efficiency of image acquisition. Experiments on virtual and real scenes demonstrate the remarkable performance of our method. Compared with the state of the art, we accomplish the planning of the photographic path with higher efficiency in a relatively simple way, achieving equivalent and even higher quality of the reconstructed model with fewer images.