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To damp the inter-area low-frequency oscillation in power system, a novel design approach of wide-area supplementary controller is presented in this paper. The reduced order state space model with dominant low frequency oscillation modes is obtained through system identification using dynamic response in power system. A matrix inequality theorem is transformed into Linear Matrix Inequality form based on variable substitution, and further, the damping controller design is converted to a cone complementarity problem solved by linearization iterative algorithm. Simulation results of test system shows that the inter-area damping controller proposed by this paper can well damp inter-area low-frequency oscillation, and is insensitive to time-delay to some degree.