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The channel estimation algorithm based on sparse Bayesian learning proposed in recent years shows better performance than the traditional channel estimation algorithm by effectively reducing the convergence error in the channel estimation process. However, the sparse Bayesian learning algorithm based on expectation maximization (EM-SBL) is difficult to meet the practical applications with low complexity and power consumption. In order to guarantee the long-term stable communication of underwater devices, this paper proposes the fast sparse Bayesian learning algorithm based on Fast Marginal Likelihood Maximization (FM-SBL) to estimate underwater acoustic channels with low power consumption and high performance. Simulation and sea trial results show the output BER after channel estimation of FM-SBL is similar to that of EM-SBL, better than LS, MP and OMP, and it has good robustness in fast and slow time-varying channels. In terms of running speed, the FM-SBL algorithm is 16.7% of EM-SBL algorithm, which greatly reduces the estimation time.