Building information modeling (BIM), a common technology contributing to information processing, is extensively applied in construction fields. BIM integration with augmented reality (AR) is flourishing in the construction industry, as it provides an effective solution for the lifecycle of a project. However, when applying BIM to AR data transfer, large and complicated models require large storage spaces, increase the model transfer time and data processing workload during rendering, and reduce visualization efficiency when using AR devices. The geometric optimization of the model using mesh reconstruction is a potential solution that can reduce the required storage while maintaining the shape of the components. In this study, a 3D engine-based mesh reconstruction algorithm that can pre-process BIM shape data and implement an AR-based full-size model is proposed, which is likely to increase the efficiency of decision making and project processing for construction management. As shown in the experimental validation, the proposed algorithm significantly reduces the number of vertices, triangles, and storage for geometric models while maintaining the overall shape. Moreover, the model elements and components of the optimized model have the same visual quality as the original model; thus, a high performance can be expected for BIM visualization in AR devices.