Abstract: In order to reconstruct 3D CT image from a set of parallel fan-beam projection data acquired at multiangles by industrial computed tomography(ICT) with line-array detector, a novel method for realizing the TV-ART algorithm was proposed. In this method, we adapted the Chambolles method and extended it to 3D condition for solving the Total Variation Minimum(TVM) of the 3D CT image, resulting in better image quality than the TV-ART using the steepest descent method or the conjugate gradient method. Meanwhile, this method was suited to implement in GPU or FPGA which was highly parallel so as to increase the calculate speed of reconstruction. The quality of 3D CT image reconstructed by our method was superior to existing methods, especial in the axial resolution.