The conception and calculation formula on torsion-warping stability function is brought forward and the torsion-warping tangent stiffness matrix of bi-axisymmetric open thin wall and lightweight beam-column element is derived for the first time, based on torsion-warping stability interpolation function. At the same time, the spatial geometric tangent stiffness matrixes for beam-column element of lightweight steel structure based on tension-compression and torsion warping stability interpolation function are presented as well.