During the long period service, it is difficult to avoid damages on the cable system of a suspension bridge. The damage of the stiffness of one side of the main cable will cause the coupling between the vertical bending and torsional degrees of freedom of the main girder, which may further affect the modal property and nonlinear response of the cable bridge under big vibration. Therefore, 7-DoFs cross section model of suspension bridge is established, considering the damage of single-side main cable stiffness. Modal analysis found that the damage of single-side main cable stiffness changed the first two natural frequency curves of the system from crossover to veering, resulting in the coupling of two independent modes. Based on this, the nonlinear vibration of the suspension bridge under internal resonance condition is calculated by the extended incremental harmonic balance method (EIHB) considering the two working conditions of damaged and undamaged main cable stiffness. The results show that the suspension bridge with damage to the stiffness of one side main cable will have 1:1 internal resonance under external harmonic excitation, and the system energy will show obvious transfer phenomenon. Under vertical and torsional harmonic excitation, the response amplitude of damaged suspension bridge is smaller than that of non-damaged suspension bridge. However, the damaged suspension bridge has two resonant response peaks, which are more sensitive to the excitation frequency. The numerical results are in good agreement with those calculated by Runge-Kutta method, which verifies the accuracy of EIHB method.