There is an inevitable effect of time delay on the stable operation of large-scale interconnected power systems. A stability analysis of wide-area power systems with multiple time delays is carried out. First, a power system model with multiple time delays is established. Second, a new Lyapunov-Krasovskii (L-K) function is constructed. This contains the coupling integral terms between multiple time delays, and a new method is used to consider the positive definiteness of the functional matrices as a whole, so that the restriction that functional matrices must be positive definite is relaxed. Then, auxiliary-function-based integral inequality is used to estimate the derivatives of the functional. This reduces the conservative of stability conditions. Finally, numerical examples of typical second-order time-delay system, single-machine infinite system and the WSCC 3-generator 9-bus are given to illustrate the effectiveness of the proposed method.