In CT-guided percutaneous punctures-an image-guided puncture method using CT images-physicians treat targets such as lung tumors, liver tumors, renal tumors, and intervertebral abscesses by inserting a puncture needle into the body from the exterior while viewing images. By recognizing two-dimensional CT images prior to a procedure, a physician determines the least invasive puncture route for the patient. Therefore, the candidate puncture route is limited to a two-dimensional region along the cross section of the human body. In this paper, we aim to construct a three-dimensional puncture space based on multiple two-dimensional CT images to search for a safer and shorter puncture route for a given patient. If all puncture routes starting from a target in the three-dimensional space were examined from all directions (the brute-force method), the processing time to derive the puncture route would be very long. We propose a more efficient method for three-dimensional puncture route selection in CT-guided percutaneous punctures. The proposed method extends the ray-tracing method, which quickly derives a line segment from a given start point to an end point on a two-dimensional plane, and applies it to three-dimensional space. During actual puncture route selection, a physician can use CT images to derive a three-dimensional puncture route that is safe for the patient and minimizes the puncture time. The main novelty is that we propose a method for deriving a three-dimensional puncture route within the allowed time in an actual puncture. The main goal is for physicians to select the puncture route they will use in the actual surgery from among the multiple three-dimensional puncture route candidates derived using the proposed method. The proposed method derives a three-dimensional puncture route within the allowed time in an actual puncture. Physicians can use the proposed method to derive a new puncture route, reducing the burden on patients and improving physician skills. In the evaluation results of a computer simulation, for a 3D CT image created by combining 170 two-dimensional CT images, the processing time for deriving the puncture route using the proposed method was approximately 59.4 s. The shortest length of the puncture route from the starting point to the target was between 20 mm and 22 mm. The search time for a three-dimensional human body consisting of 15 CT images was 4.77 s for the proposed method and 2599.0 s for a brute-force method. In a questionnaire, physicians who actually perform puncture treatments evaluated the candidate puncture routes derived by the proposed method. We confirmed that physicians could actually use these candidates as a puncture route.