The localization of acoustic sources is a parameter estimation problem where the parameters of interest are the direction of arrivals (DOAs). The DOA estimation problem can be formulated as a sparse parameter estimation problem and solved using compressive sensing (CS) methods. In this paper, the CS method of sparse Bayesian learning (SBL) is used to find the DOAs. We specifically use multi-frequency SBL leading to a non-convex optimization problem, which is solved using fixed-point iterations. We evaluate SBL along with traditional DOA estimation methods of conventional beamforming (CBF) and multiple signal classification (MUSIC) on various source localization tasks from the open access LOCATA dataset. The comparative study shows that SBL significantly outperforms CBF and MUSIC on all the considered tasks. © 2021 IEEE