Abstract: Source localization accuracy is often limited by the sampling grid. On the one hand, a coarse sampling grid has a larger modelling error, which can lead to energy leakage from the near-field to the far-field, and the leaked energy can mask the weak far-field target signal, making it difficult to estimate the direction of arrival. On the other hand, a dense sampling grid leads to high computational complexity, making the localization algorithms computationally inefficient. In order to overcome this problem, a sparse Bayesian learning based off-grid localization algorithm for mixed far- and near-field sources is proposed. An off-grid model for mixed far- and near-field acoustic sources is constructed, then the sparse Bayesian learning method is used to estimate and compensate the off-grid error, so as to overcome the grid limitation and achieve higher localization accuracy. On this basis, a grid evolution method is developed to improve the computational efficiency, which causes the grids to cover the space of interest nonuniformly, making finer grids around the position of the acoustic sources, thereby reducing the computational complexity while retaining reasonable accuracy. Numerical simulations and experimental results show that the proposed methods achieve higher localization accuracy, resolution and computational efficiency compared to the existing sparse Bayesian learning-based source localization algorithm for far- and near-field sources.