To optimize the early diagnosis and detection of lung cancer, computer-aided diagnostic (CAD) systems have been a useful tool for analyzing medical images. The temporal subtraction technique, which is a CAD system, performs the subtraction operation between the current image and the previous image on the same patient, and supports observation by emphasizing the temporal changes. However, the temporal subtraction technique for 3D images, such as thoracic CT images, has not yet been established. There is a need to develop efficient and highly accurate 3D nonrigid registration techniques to reduce subtraction artifacts. This study aims to develop a 3D nonrigid registration technique to establish a 3D temporal subtraction technique. In particular, we focus on the Finite Element Method, which is versatile, applicable to a wide range of fields, and capable of handling any shape. Our new method was examined on 46 clinical cases with multidetector row computed tomography images. As a result, the proposed method improved by 6.93% (p = 3.0 × 10−6) compared to the conventional methods in terms of the rate of reduction of artifacts, and the effectiveness was verified. Therefore, this study contributes to the literature on early detection and treatment.