In this work, we propose a spatial-temporal two-way regularized regression method for reconstructing neural source signals from EEG/MEG time course measurements. The proposed method estimates the dipole locations and amplitudes simultaneously through minimizing a single penalized least squares criterion. The novelty of our methodology is the simultaneous consideration of three desirable properties of the reconstructed source signals, that is, spatial focality, spatial smoothness, and temporal smoothness. The desirable properties are achieved by using three separate penalty functions in the penalized regression framework. Specifically, we impose a roughness penalty in the temporal domain for temporal smoothness, and a sparsity-inducing penalty and a graph Laplacian penalty in the spatial domain for spatial focality and smoothness. We develop a computational efficient multilevel block coordinate descent algorithm to implement the method. Using a simulation study with several settings of different spatial complexity and two real MEG examples, we show that the proposed method outperforms existing methods that use only a subset of the three penalty functions.