We have numerically analyzed the interaction of electron-beam (e-beam) with split-ring resonator (SRR) meta-atoms based on the simplified particle-in-cell finite-difference time-domain (PIC-FDTD) method. We have shown that narrow-band magnetic resonance can be initiated with e-beam excitation, whose resonant frequency can be tuned by structure parameters of SRRs. We have also presented that strength of magnetic resonance varies with changing the acceleration energy of e-beam in a nonmonotonous way. We have shown that there are two important factors, the interaction time and the frequency content of the magnetic field around the e-beam, which should be taken into account for the e-beam excitation. This is very different situation from that in the photo-excitation with varying the excitation intensity. This unique property for the e-beam excitation may play a crucial role in developing the terahertz (THz) devices. Our findings may open the way for the development of e-beam driven THz optical devices.