In this paper, a full discrete numerical algorithm under consideration is analyzed to a time dependent functional reaction-diffusion system and is discretized into a system of nonlinear algebra by the finite central difference, the existence of max-minimal solutions and the existence and unique property of the solution are derived by using the Gauss-Seidel numerical algorithm. Meanwhile, one simple example of the numerical computations is included to demonstrate the validity and applicability of the Gauss-Seidel numerical algorithm.