Abstract: Based on the theory of restrained torsion for a thin-walled box girder, the equations of bimoment for the restrained torsion of a thin-walled box girder under an eccentric axial load are derived through taking the eccentric axial load as a kind of a bimoment load. The practical formulas for the twist centre and principal sectoral coordinate are further derived to simplify the calculation of warping stress. A box girder model is analyzed and the calculated stresses are in a good agreement with those obtained by the shell element of the finite element software ANSYS, validating the presented method and formulas. The influence of the variation of box depth-width ratios and cantilever plate widths on the warping stress for restrained torsion of a thin-walled box girder under an eccentric axial load is analyzed in detail. It is shown that: the depth-width ratio and the cantilever plate width affect remarkably the warping stress at the tip of a cantilever plate, while they have a smaller effect on the warping stress at the intersection of web and top or bottom plates; the warping stress at the control point on the fixed end cross section of the cantilever box girder under an eccentric axial load reaches 12% of that calculated by the elementary beam theory, which should not be ignored.