This paper presents an extended integral control to the speed-governor system for damping power system oscillations. The power system oscillations mostly stem from the surplus kinetic energy which is stored in the generator during the fault period. The effective control of the surplus energy can be the most direct method to achieve the system stabilization. The LFC (load frequency control) loop can be utilized as a direct method to control the surplus energy. The proposed controller based on the extended integral control is applied to speed-governor to damp out the local and interarea mode oscillations. The proposed controller also provide good performance under presence of the singularities of speed-governor such as limits on valve position and GRC (generation rate constraints). The computer simulation has been conducted for the two-area multimachine system with various load changes. The simulation results show that the proposed controller yields much improved control performance, compared to the conventional PI controller.