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Power system stabilizers (PSS) are used to generate supplementary control signals for the excitation system in order to damp the low frequency power system oscillations. To overcome the drawbacks of conventional PSS (CPSS), numerous techniques have been proposed in the literature. Based on the analysis of existing techniques, this paper presents an indirect adaptive neural network based power system stabilizer (IDNC) design. The proposed IDNC consists of a neuro-controller, which is used to generate a supplementary control signal to the excitation system, and a neuro-identifier, which is used to model the dynamics of the power system and to adapt the neuro-controller parameters. The proposed method has the features of a simple structure, adaptivity and fast response. The proposed IDNC is evaluated on a single machine infinite bus power system under different operating conditions and disturbances to demonstrate its effectiveness and robustness.