Abstract: The traditional method of time domain Green's function (TDGF) extraction from noise cross-correlations has low resolution in a relative narrow frequency band, which affects the application of passive ocean acoustic tomography. In order to solve the problem, a method to estimate TDGF from ambient noise cross-correlations by sparse Bayesian learning (SBL) is proposed in this paper. Firstly, the sparse representation model for TDGF extraction is established, in which, the dictionary matrix consists of Fourier transform operators and the observation matrix consists of the noise cross-correlation functions in the frequency domain. Then a pre-stacking technique is adopted to compromise the resolution and the robustness of SBL for TDGF extraction. Simulation and experimental data in shallow water show that the pre-stacking-based SBL can effectively extract the arrival structure of TDGF from ambient noise with a relatively narrow frequency band, which cannot be distinguished by the traditional method, thereby a way is provided for adaptively selecting noise frequency bands to realize fast passive ocean acoustic tomography is provided.