We have numerically analyzed an electron beam (e-beam)-induced directional terahertz (THz) radiation from metamaterials. Here, we used metallic grating structures with graded depths, in which only one-way surface mode can be supported based on the spoof surface plasmon polariton (spoof SPP) concept and gives unique directional THz radiation. For numerical analysis, we used a simplified particle-in-cell (PIC) finite-difference time-domain (FDTD) method. First, we describe our simplified PIC-FDTD method in detail. Then, we show our results on the e-beam-induced directional THz radiation from graded grating with graded depths. By passing pulsed (bunched) e-beam along the grating surface, directional THz radiations are obtained from one side of the grating with shallower grooves. The direction of these radiations can be switched backward or forward by making the groove depth deeper or shallower. The spectra of these directional radiations are wideband and contain multiple sharp peaks. The deepest and the shallowest groove depths determine the lowest and the highest frequency of the radiation band, respectively. These unique radiation characteristics cannot be explained by the conventional Smith-Purcell radiation and should be attributed to the spoof SPP that originates from different locations on the graded grating.