Quadric surface is a common type of workpiece shape in industry. It can be imaged by computed tomography (CT). A sample object was scanned and its slices were reconstructed to measure its internal quadric surface. We used the U-net image segmentation network to obtain the interested region and then detected the edge in the segmentation results and obtained curve fitting results. The curves were stacked into a three-dimensional point set. The three-dimensional spatial coordinate information for the internal quadric surface was computed through surface fitting. The results demonstrate that the proposed method can effectively extract the internal quadric surface parameters, and the fitting error can be controlled within 1%, which is superior to that achieved with a traditional algorithm.