A study has been carried out on the robust stability problem related to time delay in power systems. Firstly, a power system model is established with time delay taken into consideration. Next, by constructing the delay-product-type augmented Lyapunov-Krasovskii functional, a new low conservatism stability criterion can be obtained with the free-matrix-based integral inequality method adopted to define the derivative of the functional. Finally, the effectiveness of the proposed method is verified by a single-machine infinite system, a 4-generator 11-bus power system and a typical second-order system.