Simultaneously considering shear deformation and second-order effects to analytically calculate the critical load of a structural member is a challenging task in solving the variable coefficient critical differential equation. In this study, a finite element method was used to derive the stiffness matrix of a variable cross-section element. Third-order Hermite interpolation functions and third-order Lagrange interpolation functions were used to calculate the bending deformation and inertia moment changes within the element. Linear interpolation functions were used to calculate the shear deformation and cross-sectional area changes within the element. By using the minimum potential energy principle to vary the total potential energy, the stiffness matrix of the variable cross-section component element incorporating bending deformation, shear deformation, and axial force second-order effects was determined. Finally, the self-developed finite element program was used to perform calculations on the case studies. The research results indicate that this algorithm has good computational accuracy and can analyze the second-order displacement amplification factor and the support effects between variable cross-section portal steel frame columns.