This paper presents a free-weighting matrix (FWM) method based on linear control design approach for the wide-area robust damping (WARD) controller associated with flexible AC transmission system (FACTS) device to improve the dynamical performance of the large-scale power systems. First, the linearized reduced-order plant model is established, which efficiently considers the time delay of the remote feedback signals transmitted by wide-area measurement systems. Then, based on the robust control theory, the design of the FACTS-WARD controller is formulated as the standard control problem on delaydependent state-feedback robust control, which is described by a set of linear matrix inequality constraints. Furthermore, in order to obtain the optimal control parameters that can endure the maximum time delay, a FWM approach is proposed to solve the time-dependent problem of the time-delay system. Meanwhile, an iterative algorithm based on cone complementary linearization is presented to search out the optimal control parameters. Finally, the nonlinear simulations on the 2-area 4-machine and the 5-area 16-machine test systems are performed, to evaluate the control performance of the proposed robust wide-area time-delay control approach.