A model of a room impulse response (RIR) is useful for a wide range of applications. Typically, the early part of an RIR is sparse, and its sparse structure allows for accurate and simple modeling of the RIR. The existing L-p (0 < p ≤ 1)-norm-based methods suffer from the sensitivity to the user-selected regularization parameters or a high computational burden. In this work, we propose to reconstruct the sparse model for the early part of RIRs with sparse Bayesian learning (SBL). Under the framework of SBL, the proposed method can adaptively learn the optimal hyper-parameters from data at a low computational cost. Experiment results show that the proposed method has advantages in terms of noise robustness, reconstruction sparsity, and computational efficiency compared to the existing methods.