This paper presents the application of the matching pursuit method to model synchronous generator. This method is useful for online analysis. In the proposed method, the field voltage is considered as input signal, while the terminal voltage and active power of the generator are output signals. Usually, the difference equation with a second degree polynomial structure is used to estimate the corresponding parameters of the regressor matrix. This matrix contains the elements of the difference equation for all sampling intervals. However, the number of parameters that should be estimated increases significantly with the increase in the difference equation order. In this paper, the matching pursuit method is implemented to identify important parameters with a very good accuracy and in a shorter time. In order to show the effectiveness of the proposed algorithm, it is applied to a nonlinear generator and the required signals are sampled using a phasor measurement unit (PMU). The simulation results show the effectiveness and precision of the proposed method.