In order to solve the problem that for general composite frame consisting of concrete-filled steel tubular (CFT) columns and steel-concrete composite beams (CB), the method to achieve strong column-weak beam behavior is not available in China code, GB 50011—2010, Pushover method was applied to study the damage mechanism of the CB-concrete-filled square steel tubular (CFST) column frame. The influence of ultimate moment ratio (column to beam) and beam-column line stiffness ratio on the structural yield mechanism was discussed. The analysis results showed that the method by adjusting the elastic inner force for RC frame can not give a guarantee to fulfill the strong column-weak beam yield mechanism. Furthermore the design formula to make sure the strong column-weak beam mechanism of CB-CFT column frames was preliminarily suggested, which could offer some valuable references in design of composite frame structures.