Abstract: In order to determine the position of the torsional center of a beam of arbitrary complex non-circular section, the shape of all the out-of-plane deformation of the beam of non-circular section caused by non-uniform torsion is expressed by the nodal-line method as a family of surfaces containing unknown functions of the nodal lines. After establishing the governing equations of the beam caused by its non-uniform torsion, the numerical solutions of these unknown functions are obtained by using an ODE (ordinary differential equation) solver for a torque and a transverse load separately. Finally, the position of the torsional center of the beam of a complex cross section is derived by using the principle of stiffness equivalence. The computational results of examples show that the method is reliable for computing the torsional center position of a beam of arbitrary complex non-circular section.