A prerequisite of thoracic radiotherapy planning is the accurate modeling of respiratory motion of thoracic structures. While the emergence of 4D imaging techniques makes it possible to visualize the anatomic changes during the respiratory process, attaining accurate voxel-to-voxel correspondence between different breathing phases remains to be a challenging task. We mainly study the deformable registration in thoracic radiotherapy, using the fast free-form deformable (FFD) registration strategy with total-variation regularization in consideration of the discontinuous movements of the involved anatomic structures. We describe the registration problem as minimizing an energy function that includes both similarity and smoothness metrics. By using calculus of variations, the minimization problem was represented as a set of nonlinear Euler-Lagrange partial differential equations (PDEs). Finite difference scheme, tri-linear interpolation and Newton iteration were used to solve the PDE, figuring out the displacement field. The performance of the proposed technique was demonstrated by using a 2D thoracic image, a 3D CT volume of lungs and three 3D MRI volumes of fetus. A comparison with the Levenberg-Marquardt least square optimization and 2norm regularization method showed that the registration accuracy was markedly improved, and our technology can handle the registration including organs' discontinuous movements better. Combining the properties of preserving the image edges of TV norm and huge degrees of freedom (DOF) of FFD, our method is fast, accurate and fully automatic. Given the increased interest in 4D thoracic radiation therapy, the deformable registration method described here should find useful application in future clinical practice.