To infer brain source activation patterns under different cognitive tasks is an integral step to understand how our brain works. Traditional electroencephalogram (EEG) Source Imaging (ESI) methods usually do not distinguish task-related and spurious non-task-related sources that jointly generate EEG signals, which inevitably yield misleading reconstructed activation patterns. In this research, we argue that the taskrelated source signal intrinsically has a low-rank property, which is exploited to to infer the true task-related EEG sources location. Although the true task-related source signal is sparse and low-rank, the contribution of spurious sources scattering over the source space with intermittent activation patterns makes the actual source space lose the low-rank property. To reconstruct a low-rank true source, we propose a novel ESI model that involves a spatial low-rank representation and a temporal Laplacian graph regularization, the latter of which guarantees the temporal smoothness of the source signal and eliminate the spurious ones. To solve the proposed model, an augmented Lagrangian objective function is formulated and an algorithm in the framework of alternating direction method of multipliers is proposed. Numerical results illustrate the effectiveness of the proposed method in terms of reconstruction accuracy with high efficiency.