Electroencephalography (EEG) and Magnetoencephalography (MEG) are pivotal in understanding brain activity but are limited by their poor spatial resolution. EEG/MEG source imaging (ESI) infers the high-resolution electric field distribution in the brain based on the low-resolution scalp EEG/MEG observations. However, the ESI problem is ill-posed, and how to bring neuroscience priors into ESI method is the key. Here, we present a novel method which utilizes the Brain Geometric-informed Basis Functions (GBFs) as priors to enhance EEG/MEG source imaging. Through comprehensive experiments on both synthetic data and real task EEG data, we demonstrate the superiority of GBFs over traditional spatial basis functions (e.g., Harmonic and MSP), as well as existing ESI methods (e.g., dSPM, MNE, sLORETA, eLORETA). GBFs provide robust ESI results under different noise levels, and result in biologically interpretable EEG sources. We believe the high-resolution EEG source imaging from GBFs will greatly advance neuroscience research.