In this paper, a sensitivity matrix based approach is proposed to improve the minimum damping ratio. The proposed method also avoids burdensome deviation calculations of damping ratio of large-scale power grids when compared to the Small-Signal-Stability Constrained Optimal Power Flow (SSSC-OPF) approach. This is achieved using the Matrix Perturbation Theory (MPT) to deal with the 2nd order sensitivity matrices, and the establishment of an optimal corrective control model to regulate the output power of generating units to improve the minimum damping ratio of power grids. Finally, simulation results on the IEEE 9-bus, IEEE 39-bus and a China 634-bus systems show that the proposed approach can significantly reduce the burden of deviation calculation, while enhancing power system stability and ensuring calculation accuracy.