The strong coupling phenomenon between surface plasmons and quantum emitters has received extensive attention in recent years. It is usually studied by the far-field spectral detection method such as scattering, absorption, and fluorescence. In the electron energy loss spectroscopy (EELS), highly focused electron beams are used for implementing the local detection on a sub-nanometer scale, which can be more effective to study strong coupling. In this work, the electron energy loss spectrum of silver nanorods, dielectric materials and their composite core-shell nanostructures are theoretically simulated respectively, and the energy and mode characteristics of surface plasmons on the silver nanorods and the excitation characteristics of dielectric materials are obtained. The electron energy loss spectrum of surface plasmon is basically consistent with the related experimental result. Rabi splitting of spectral peaks is observed in the electron energy loss spectra of the above composite structures, and the effect of Ag nanorod size on Rabi splitting is explored. The strong coupling between the radiative dipolar and non-radiative higher-order plasmon with the excitation of the dielectric materials in the infrared and visible band is discussed, and the corresponding dispersion relation is analyzed with the coupled oscillator mode. Furthermore, the plexciton caused by strong coupling are discussed from the perspective of spatial distribution of loss spectrum imaging. Our study builds the basis for further theoretical study, and can guide the further experimental research.