Acoustic localization is often difficult to obtain high-resolution results for low-frequency source. This paper presents a Bayesian sparsity-regularization approach to solve the above problem to some extent. Such a sparsity prior distribution is a probability hypothesis added to unknown targets. This paper implements Student-t prior to sparsity regularization. In this sense, more physical information is properly added to make the ill-posed inverse problem less uncertainty and more meaningful in modeling. Through simulations and experiments, proposed approach can obtain more robust localization at as low as 1000Hz Hz with -1dB SNR.