The direct injection of CO_2 into the deep ocean with a pipe towed by a moving ship is considered to be a feasible way to mitigate global warming and expected to minimize its environmental impacts on marine organisms in the vicinity of the injection points. In this study, a numerical study was carried out for the dispersion of CO_2 concentration in the deep ocean by using a fixed mesoscale and a moving small-scale grid systems, where the nested small-scale domain moves in the mesoscale domain along the trajectory of the moving ship. To overcome the artificial diffusion of mass concentration at the interfaces of two different grid systems, a particle diffusion model was developed for anisotropic diffusion in the ocean. The developed techniques demonstrated its efficiencies and applicability to give an outline for the optimization of the CO_2 ocean sequestration system, by which biological impacts should be minimized and insignificant.