Abstract: Using the weak convergence theorem of T. G. Kurtz and the Liapunov stability theory of multi-dimensional systems, we discuss the weak convergence of the nonlinear multi-dimensional jump processes,\sqrtN\left(x_N-\hatx\right) to one diffusion process, where x_N is reaction-diffusion process, N the reaction volume, and \hatx the stable state of the correspondent deterministic system.