High-order spoof surface plasmon (SSP) mode on corrugated metallic surfaces can find many interesting applications, such as in imaging, sensing, transmission and enhanced radiation source, etc. In this paper, an efficient excitation method of the high-order SSP mode by using an injected electron beam on the uniform rectangular metallic grating is proposed and investigated numerically. Based on the matched wave momentum between the SSP mode and the electron beam, both the fundamental and high-order SSP modes can be excited on the structure by using a single injected electron beam. Numerical simulation results indicate that the maximum electric field intensity of the generated high-order SSP mode is about two orders higher than that of the fundamental SSP mode. In addition, the peak power of the excited high-order SSP mode is almost two times that of the fundamental SSP mode power by the same energy electron beam, which demonstrates the obvious advantage of the high-order SSP electronic excitation approach compared to the previous fundamental SSP mode excitation on the structure. The central working frequency of high-order SSP power spectrum is about three times that of the fundamental SSP power spectrum. Moreover, the influences of the injected electron beam energy on the excited SSP power spectrum are analyzed specifically. It is shown that the generated SSP power spectrum demonstrates a blue shift with the decreased working voltage of the electron beam simultaneously, with its peak power increasing. However, the working bandwidth is narrowed with decreased beam voltage, which further reveals its working mechanism of presented electronic excitation of the SSP mode. The presented studies provide a new method to excite a high-order SSP mode on the metallic grating, which can find some potential applications in high-sensitivity sensing, deep sub-wavelength waveguide, and many others in terahertz spectra.