Recent research on sparse signal reconstruction (SSR) shows that the sparse Bayesian learning (SBL) method is one of the most popular methods for direction-of-arrival (DOA) estimation. However, the high computational complexity and the time-consuming iterations in the Bayesian learning make the SBL-based methods difficult in practical applications. To address this problem, the iterative process in the SBL method is improved in this paper. Inspired by the spatial sparsity of the signal variance, an l 0 norm constraint Bayesian strategy for DOA estimation is proposed. An additional l 0 norm penalty is integrated into the objective function of the signal variance vector to achieve zero attraction. With a few user-adjusted parameters, the proposed strategy achieves a faster implementation while inheriting the superior performance of the SBL method for DOA estimation. Numerical simulations demonstrate that the proposed strategy can significantly improve the convergence rate and accelerate the iterative process. The innovative work increases the possibility of real-time implementation. [ABSTRACT FROM AUTHOR]