Abstract: In underwater acoustic Single-Carrier Frequency Domain Equalization communications, the performance of channel estimation is often interfered by ambient noise. To solve the problem, a channel estimation method with low complexity is proposed. Firstly, Considering the sparseness of underwater acoustic channels in time domain, the relationship among the frequency-domain input and output signals and the channel impulse response is derived, and by introducing a sparsity-inducing regularizer, the objective function for sparse channel estimation is constructed. Then optimize the objective function iteratively with separable approximation, and by sparsification and debiasing, the final esimate of the channel transfer flmction is obtained. Finally, numerical simulation and sea-trial data are used to evaluate the performance and the computation efficiency of the proposed method, demonstrating that the proposed method outperforms the classical channel estimation methods in the aspects of estimation accuracy and computation complexity.