The regular molecular dynamics method cannot simulate the ion concentration gradient system because the number of particles in the system is constant during the simulation. In the present study, in order to overcome the above problem, we developed a new nonequilibrium molecular dynamics simulation program, which can be applied to the concentration gradient system, such as the ion diffusion in the solid state ionics materials. Moreover, we applied our new program to the LiCoO2 system that has been used as a cathode material of the lithium battery. The new program succeeded to reproduce the lithium ion diffusion process from the higher concentration area to the lower concentration area and, hence, we confirmed the high ability of our new program to the simulation of the ion concentration gradient system.