Metal cylindrical shaft parts are critical components in industrial manufacturing that require high standards for roundness error and surface roughness. When using the self-developed multi-beam angle sensor (MBAS) to detect metal cylindrical shaft parts, the distorted multi-spots degrade the measurement accuracy due to the nonlinear distortion caused by the metal material's reflective properties and surface roughness. In this study, we propose a spot coordinate prediction network (SCPNet), which is a deep-learning neural network designed to predict spot coordinates, in combination with Hough circle detection for localization. The singular value decomposition (SVD) model is employed to eliminate the tilt error to achieve high-precision, three-dimensional (3D) surface reconstruction of metal cylindrical shaft parts. The experimental results demonstrate that SCPNet can effectively correct distorted multi-spots, with an average error of the spot center of 0.0612 pixels for ten points. The proposed method was employed to measure metal cylindrical shaft parts with radii of 10 mm, 20 mm, 35 mm, and 50 mm, with resulting standard deviation (STD) values of 0.0022 µm, 0.0026 µm, 0.0028 µm, and 0.0036 µm, respectively.