Apart from its fundamental importance, ionization phenomenon of atoms by impact of energetic charged particles has practical applications in various kinds of plasmas, in radiation physics and in the study of penetration of charged particles through matter. Compared with other processes, this particular reaction helps to reveal many details about the dynamical process and the level population, and, in fact, can provide a new insight into and a promising route to studying the e-p interactions in the presence of Coulomb field. The development of ion sources producing multiply charged ions and of antiproton beams allow us to change the potentials and hence the whole final momentum distribution. A great variety of experimental conditions allowed by changing the projectile charge and velocity constitute a stringent test for theory. The continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximation model has emerged as a reliable method to compute cross sections for different projectile/target combinations from intermediate to high non-relativistic impact energies. This model is of the first order in a distorted-wave series. It takes into account the long-range behaviour of the Coulomb potential and includes the distortion of the target states in both the initial and final channels. In the present work, the single different cross sections (SDCS), double different cross sections (DDCS), and total cross sections for single ionization of 1s, 2s and 2p shell of Ne atom by impact of proton are calculated in the framework of continuum-distorted-wave (CDW) method and the CDW-EIS approximation model, respectively. The influence of the eikonal-initial-state on the cross section, and the mechanism of the proton-atom collision ionization are discussed in detail. Moreover, the structures of the SDCS and DDCS of each shell are studied and the ionization mechanism of soft collision, electron capture to the continuum state, binary encounter collision are demonstrated. Our results show that for the 2p shell of Neon, as the incident proton energy increases, the region of the SDCS becomes larger and the soft ionization turns dominant in the low energy region. The eikonal-initial-state effect on the cross section is obvious in the lower energy region, yet smaller as the incident energy increases. These effects on the DDCS are greater than on the SDCS. The present CDW-EIS and CDW results are compared with the experimental data available in the energy range of 1-5000 keV/u for H+ on Ne in the literature, showing that they are quantitatively in good agreement. In general, the CDW-EIS describes well the multiple ionization above 50 keV/u, showing a clear tendency to coalesce with the CDW at high energies.