Electroencephalography (EEG) provides high temporal resolution neural data for brain-computer interfacing via noninvasive electrophysiological recording. Estimating the internal brain activity by means of source imaging techniques can further improve the spatial resolution of EEG and enhance the reliability of neural decoding and brain-computer interaction. In this work, we propose a novel EEG data-driven source imaging scheme for precise and efficient estimation of macroscale spatiotemporal brain dynamics across thalamus and cortical regions with deep learning methods. A deep source imaging framework with a convolutional-recurrent neural network is designed to estimate the internal brain dynamics from high-density EEG recordings. Moreover, a brain model including 210 cortical regions and 16 thalamic nuclei is established based on human brain connectome to provide synthetic training data, which manifests intrinsic characteristics of underlying brain dynamics in spontaneous, stimulation-evoked, and pathological states. Transfer learning algorithm is further applied to the trained network to reduce the dynamical differences between synthetic and realistic EEG. Extensive experiments exhibit that the proposed deep-learning method can accurately estimate the spatial and temporal activity of brain sources and achieves superior performance compared to the state-of-the-art approaches. Moreover, the EEG data-driven source imaging framework is effective in the location of seizure onset zone in epilepsy and reconstruction of dynamical thalamocortical interactions during sensory processing of acupuncture stimulation, implying its applicability in brain-computer interfacing for neuroscience research and clinical applications.