Fully nonlinear shock waves (SW) structure of ion-acoustic waves are investigated in a three-component cold plasma consisting of two positive ions fluids and non-thermal electron distribution. The physical parameters in the system, such as ion density ratios, furthermore, they play an important role in the profile of the small amplitude ion-acoustic SW. Using m-KdV, the basic equations are reduced to one evolution equation. The latter has been analyzed and solved numerically to obtain an arbitrary amplitude shock wave profile as well as the possible regions for the existing waves. We present a negative potential, which corresponds to a compressive wave profile. The findings of this investigation are used to interpret the electrostatic waves that may be observed in the Mars ionosphere. If we observe this wave in Mars's ionosphere, we will be able to explain how the gas has been lost from the ionosphere if we get to the physical meaning of it.