Circular cone-beam computed tomography (CT) is a popular configuration in industrial non-destructive testing. Corresponding to the circular cone-beam CT, the Feldkamp, Davis, and Kress (FDK) algorithm is the most popular reconstruction method. However, in the case of large cone angle scanning, the slice artifacts of the reconstruction using the FDK algorithm are visible because the data collected with the circular orbit scan mode do not satisfy the completeness conditions for exact reconstruction. To solve the problem, this study proposed a hybrid FDK (H-FDK) algorithm using a method that combines variable filtering and conjugate rays. First, the shape and curvature of the detector were changed for the filtering paths to be variable. Then, the conjugate weighting function for backprojection was constructed. Subsequently, optimization experiments were conducted to find optimal parameters for the detector and conjugate weighting function. Finally, the comparative experimental results demonstrated that the slices reconstructed by the H-FDK algorithm produced a discernible quality improvement.