We report the experimental results of proton acceleration as well as the simple one-dimensional model which explains our experimental data. The proton acceleration experiment is carried out with a TW short pulse laser irradiated on a tantalum thin-foil target (3 μm thickness) with an intensity of ∼3×1018 Wcm−2. Accelerated protons exhibit a typical energy spectrum with two quasi-Maxwellian components with a high energy cut-off. We can successfully explain the higher energy part as well as the cut off energy of the proton spectrum with the simple-one-dimensional model based on the strong charge separation regime, which is the extension of the model proposed originally by [M. Passoni et al., Phys. Rev. E 69 (2004) 026411].