Underwater acoustic (UA) channel is often affected by strong impulsive noise. In this paper, a compressive sensing based iterative algorithm is proposed to accurately estimate the channel state information and mitigate the impulsive noise, which is important to ensure high-speed data transmission in UA orthogonal frequency-division multiplexing communication systems. By exploiting the sparsity of the impulsive noise and channel impulse response in the time domain, we adopt the orthogonal matching pursuit algorithm to improve the accuracy of channel estimation with relatively low computational complexity. The proposed algorithm is evaluated through numerical simulations and real data collected during a UA communication experiment conducted in December 2015 in the estuary of the Swan River, Western Australia. The results show that the proposed algorithm has a better performance than existing approaches.