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Fan noise has become an important noise component of civil aviation engines with the increasing bypass ratio. The mode identification method is the key to in-duct fan noise testing. The number of modes that can propagate through the duct increases dramatically for high-frequency in-duct fan noise, which requires a large number of microphones to measure the sound field in the duct. Since the number of modes is usually larger than the number of microphones, it is difficult to realize mode identification. A Sparse Bayesian Learning algorithm for mode identification is proposed to solve this problem in this paper. The in-duct sound field is described by a statistical model, and the inverse problem of mode identification is expressed in a Bayesian framework. The non-convex optimization problem of the cost function is considered, iteratively achieving the sparsest solution via a block coordinate descent algorithm in a majorization-minimization framework. The mode identification method based on Sparse Bayesian Learning has high sparsity and can achieve parameter adaptation. The effectiveness of the Sparse Bayesian Learning method for duct mode identification is verified by numerical simulations and experimental tests. The results show that the mode identification method of Sparse Bayesian Learning can accurately identify the target mode using fewer microphones. • Applying the Sparse Bayesian Learning (SBL) method for mode identification, the strong sparse induction performance of the SBL method is better at suppressing the non-target modes and identifying accurate sparse target modes. • The sparsest mode coefficient amplitudes are solved indirectly by estimating the hyperparameters. The optimal parameters can be determined adaptively by iterations without the need for manual selection of parameters. • It is verified through numerical simulations and experimental tests that the mode identification method of SBL can accurately identify target modes with a small number of microphones, and its results have strong sparsity and robustness. [ABSTRACT FROM AUTHOR]