Abstract: The single-trial extracting of evoked potential (EPs) has become a vexed question in the process of electroencephalogram owing to the faint signal-to-noise ratio (SNR) of EP. Sparse reoresention is a powerful tool in signal denoising, and EPs have been proven to strong sparsity over an appropriate dictionary. In this paper, we present a novel sparse representation and autoregressive model with exogenous input modeling (ARX) approach to solving the EPs extraction problem. The extraction process of evoked potentials are performed in three stages. First, we utilize an reference ongoing spontaneous Electroencephalogram to identify the parameters?of?the autoregressive model. Second, instead of the moving average model, sparse representation is used to model the EP in the autoregressive-moving average model. Finally, we calculate the sparse coefficients and derive evoked potentials by using the autoregressive model. Utilizing the synthetic EEG data and real visual evoked potentials data to estimate the performance of this method, our algorithms has?been proven highly?effective in the experiment results. Comparing with MOSCA and ARX, our method can estimate the latency and amplitude accurately, even in low SNR environments.