A new CT reconstruction method, that is the second-order difference transformation (SODT) algorithmis introduced. It can reconstruct CT image without artifacts and determine the kinds of the materials simultaneously from a single radiograph. Otherwise, it is much faster than other reconstruction approaches, like filtered back-projection method (FBP) and algebraic reconstruction technique (ART). Although it requires strong prior knowledge, there is no requiring of the symmetry of the object to utilize this approach. So the SODT method is very suitable for X-ray or industrial CT inspection, where many objects have nearly circular symmetry, especially for inspecting material, structure, thickness and defect etc.