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In many mathematical models, positivity is one of the attributes that must be possessed by the continuous systems. For instance, the unknown quantities in the Brusselator reaction-diffusion model represent the concentration of two reactant species. The negative values of concentration produced by any numerical methods is meaningless. This work is concerned with the investigation of a novel unconditionally positivity preserving finite difference (FD) scheme to be used for the solution of three dimensional Brusselator reaction-diffusion system. Von Neumann stability method and Taylor series expansion is applied to verify unconditional stability and consistency of the proposed FD scheme. Results are compared against well-known forward Euler FD scheme and some results reported in the literature.