Reconstruction algorithm is the core technology in computerized tomography (CT). It is intractable to utilize priori information and constraint condition in analytical CT reconstruction algorithm. To resolve the problem, by analyzing the principle of the filtered backprojection (FBP) reconstruction algorithm, the relationship between the ideal CT image and the reconstructed CT image is proposed, an iterative method based on FBP is put forward. To suppress the spot artifacts induced by the iterative algorithm, a total variation (TV) model is introduced into the procedure and a TV constrained iterative filtered backprojection is built. In numerical simulation, images reconstructed by this method show high consistency with the ideal image, whether the sinograms are ideal, sparse, metal or limited angle. The results indicate that it is an adaptable and high precision CT reconstruction method.