Three-dimensional (3D) geological modeling is a process of interpretation that integrates multiple source inputs and knowledge into geometry to represent the understanding of geologists. When geologists build a high-quality 3D geological model, this process still involves some issues such as sparse drillhole data, imperfect prior knowledge, and sensitive modeling algorithms. Therefore, taking uncertainty as the measurement criterion for the variation extent of the posterior likelihood of the 3D geological model and assisting in increasing the quality of the model are crucial issues in this domain. This paper proposes a novel method based on a (1 + ε)-approximation global optimum strategy, which is a type of big data and machine learning technique, to determine and present the uncertainty hidden in geometry. Compared with previous approaches, our strategy made the following new contributions: (1) the global optimum solution calculated by potential models is utilized to represent the uncertainty at each location; (2) the strategy offers a quantifiable reliability to each model that is involved in the evaluation process, and values of reliability are unknown before the commencement, meaning that they do not depend on expert experience; moreover, they can also be verified by comparing prior knowledge with information that such 3D models possess; (3) compared with previous studies, the number of perturbing models is no longer a key prerequisite for this kind of study to evaluate the quality of one geological model, thereby greatly reducing the computational complexity and improving the practicability. Finally, a case study was conducted to assess the uncertainty of a real 3D geological model in northwest Hunan Province, China.