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This paper presents construction of Lyapunov functions for power systems in the presence of SVC based on solving the Linear Matrix Inequality (LMI) derived from the Lyapunov stability theorem considering the AVR control system and SVC in two control strategies. The proposed Lyapunov function is constructed as a quadratic form of state variables and an integral term which satisfies the sector condition. Two-machine one-load system in the presence of SVC is considered. The critical clearing time (CCT) of power system with common mode and transient mode of SVC can be calculated by Lyapunov function. To verify the proposed Lyapunov function, the transient stability assessment is shown for comparison.