Three-dimensional (3D) measurement that captures the state of construction sites is key to promoting ICT-supported construction processes. Structure-from-Motion (SfM) and Multi-View Stereo photogrammetry are the best solutions for small and mid-sized construction companies due to their high portability and low cost. However, efficient creation of high-quality 3D dense models using photogrammetry is difficult for site workers because the model quality relies heavily on manually selected camera poses. To address this issue, we propose a photogrammetry process that improves the quality and efficiency of 3D dense model reconstruction to measure construction sites. The proposed process begins with a small initial photo set. Then, a computer-supported best-view guidance system predicts the geometric quality of the dense model, estimates the best target positions for additional photographs using SfM results, and provides workers with that position information. The effectiveness and efficiency of the process and system were evaluated at a real-world construction site. The evaluation demonstrated that the process and system can prevent capturing unnecessary images, improve the efficiency of the on-site photographic work, and generate a dense model with quality assurance. We also found that a smartphone camera is the most suitable device for implementing the process.