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Diffusion, transport of mass in response to concentration and thermal energy gradient, is an important transport property, vital in material science and life science. In the present work, we have studied about the diffusion of zwitterion glycine, zwitterion diglycine and zwitterion triglycine in SPC/E model of water using classical molecular dynamics. Self and binary diffusion coefficients of aqueous solution of these molecules have been estimated using Einstein's method. Our results agree with experimental data reported in literatures. Temperature dependency of diffusion of glycine in water has been explored using estimated values of self and binary diffusion coefficients at four different temperature. Effects of peptide bond formation in diffusion has been studied using peptide chain composed of up to three monomers of glycine. The system-size dependence of diffusion coefficient has been studied and the shear viscosity of solvent and system has been calculated. Also, the diffusion coefficient of zwitterion glycine in other water model TIP4P/2005 has been estimated. The structure of the system has been analyzed using radial distribution function of different atoms. [ABSTRACT FROM AUTHOR]