The section of the column under axial compression used in a certain electrostatic precipitator is composed of double H shaped steel limbs and the stiffened connecting web by weld. As the width of connecting web usually exceeds 3 times of the section height of H shaped steel, the axis which connecting web lies in is the weaker axis for the stiffness of column section, while the midperpendicular of connecting web is the stronger axis. In consideration of initial geometrical imperfections and weld residual stresses, the study on stability round the stronger axis of column subjected to axial compression by nonlinear finite element method is conducted. The research results indicate that the column doesn’t present the flexural buckling round the stronger axis, but present the elasto-plastic flexural-torsional buckling. A buckling factor is produced to measure the stability performance of column round stronger axis. When the connecting channel shaped steels between two limbs and the stiffeners located on connecting web are strengthened, the buckling factor increases slightly. When the width-thickness ratio of connecting web increases, the buckling factor decreases significantly. When the slenderness of H shaped steel round the stronger axis is kept constant and the height-thickness ratio of H-shaped steel web increases, the buckling factor increases. Based on a great many computation results, the regressed recommendation is proposed how to evaluate the design buckling bearing capacity of column under axial compression round stronger axis.