In order to further study the radiation of the relativistic electron beam-ion channel experimentally and theoretically, the propagation of a relativistic electron beam in neutral gas and its self-focusing process are investigated. Particle in cell (PIC) simulation shows that the electron beam can self-focus and transmit the dynamically loaded plasma through impact ionization. The transverse and the longitude inhomogeneities of the ion background have significant effects on the transport properties of the electron beam. Base on these researches, a model of transmission of electron beam in a transverse non-uniform ion background is supposed. And the condition of self-focus is given. The numerical results show that the transverse inhomogeneity will lead to the mixed phase transmission of the electron beam, and the inner electrons can defocus near the focus point, which is consistent with the PIC simulation. The PIC simulation also shows that due to the self-focusing of the electron beam, there are much more ions to be ionized at the focus point, which will capture the lower-energy electrons after collision, the capture electron effect will significantly reduce the efficiency of the transmission of the electron beam. But the distribution of the captured electrons in the longitude direction is quasi-periodic, which acts as the electrostatic Wiggler field. These may achieve the dynamical loading of the electrostatic Wiggler field. These results give new clues to the further study of electron beam-plasma system in experiment and the establishment of theoretical models.