In China, increasing the application ratio of hot-rolled H-shapes has become a severe problem that the government, academia, and engineering circles must vigorously address. Research on reasonable hot-rolled H-shapes built-up columns is one of the primary methods. After reviewing the various combination columns in the existing research, the paper proposes the new flanged cruciform H-shapes columns (FCHCs) made of three hot-rolled H-shapes. Using comprehensive imperfections given by the design standard, GB50017-2017, the paper analyzes the global buckling of FCHCs subjected to the axial compression load. The global buckling factor obtained is compared with the current national design code. Comparative analysis of seventy-two specimens of Q345 and Q460 steel found that the global buckling mode of FCHCs was flexural bending buckling around the axis of symmetry, and global torsional buckling and local buckling did not occur. Furthermore, the corresponding column curves in current design codes overestimate the dimensionless buckling strength of the novel FCHCs. Therefore, designers need to drop a class to select the global buckling factor within a specific range. Finally, new column global buckling curves are proposed based on a non-linear fitting of the numerical results according to the current national design codes.