Abstract: The impulsive noise and carrier frequency shift affected and limited the performance of underwater acoustic system based on orthogonal frequency division multiplexing (OFDM) seriously. A new algorithm based on sparse Bayesian learning (SBL) was presented to estimate the impulse noise and carrier frequency offset jointly. In each iteration of the proposed method, the corresponding carrier frequency shift value was estimated and then taken to have a compensation for the received signals by using null tones, according to the minimum mean square error (MMSE) estimate of impulse noise, which was firstly got by all the tones and a posterior probability of the received frequency domain signals, and this way could reduce the influence between these two kinds of common interference availably. The simulation results verify that the new algorithm has lower bit error ratio (BER) compared to the several existing separate estimation algorithms, and improves the robustness of underwater acoustic communication system in the presence of non-Gaussian noise.