In this paper a synchronous multi-particle cellular automaton model of diffusion with self-annihilation is developed based on the multi-particle cellular automata suggested previously by other authors. The models of pure diffusion and diffusion with self-annihilation are described and investigated. The correctness of the models is tested separately against the exact solutions of the diffusion equation for different 3D domains. The accuracy of the cellular automata simulation results is investigated depending on the number of cells per a single physical unit. The calculation time of cellular automaton simulation of diffusion with self-annihilation is compared with the calculation time of the Monte Carlo random walk on parallelepipeds method for different domain sizes. The parallel implementation of the cellular automaton model is developed and efficiency of the parallel code is analyzed.