Structural control and heath monitoring is of particular importance. Columns are one of the most important structural elements, and compared to other elements, the spread of local damage, however small, can lead to premature destruction of the structure. A damaged column may have buckling instability due to an axial force less than the critical load of the healthy condition of the column; therefore, the column damage detection under the effect of axial load is important. In this paper, the column in healthy conditions and damage due to different ratios of base critical load were frequency analyzed in ABAQUS software and modal responses were extracted. Studies have shown that with increasing load, the frequency values decrease. Additionally, at the same load ratios, the healthy state frequency is higher than the damaged state frequency. Then, the curvature of the primary and secondary shapes of the vibration modes was calculated. Based on computational primary and secondary curvatures, DI1 and DI2 damage detection indices were defined. The damage detection results of curvature indices showed the optimal performance of these indices in detecting damage locations, with the difference that the DI1 index shows possible damage locations and the detection is associated with uncertainty. The results also showed that the curvature index of damage detection in one damage location is not affected by changes in damage severity in other damage locations. Additionally, the axial load has no effect on the curvature index of damage detection and this index is affected by support conditions, section area and damage severity.