Accurate reconstruction of the brain activities from electroencephalography and magnetoencephalography (E/MEG) remains a long-standing challenge for the intrinsic ill-posedness in the inverse problem. In this study, to address this issue, we propose a novel data-driven source imaging framework based on sparse Bayesian learning and deep neural network (SI-SBLNN). Within this framework, the variational inference in conventional algorithm, which is built upon sparse Bayesian learning, is compressed via constructing a straightforward mapping from measurements to latent sparseness encoding parameters using deep neural network. The network is trained with synthesized data derived from the probabilistic graphical model embedded in the conventional algorithm. We achieved a realization of this framework with the algorithm, source imaging based on spatio-temporal basis function (SI-STBF), as backbone. In numerical simulations, the proposed algorithm validated its availability for different head models and robustness against distinct intensities of the noise. Meanwhile, it acquired superior performance compared to SI-STBF and several benchmarks in a variety of source configurations. Additionally, in real data experiments, it obtained the concordant results with the prior studies.