Self-diffusion coefficients of exponential-six fluids are studied using equilibrium molecular dynamics simulation technique. Mean-square displacements and velocity autocorrelation functions are used to calculate selfdiffusion coefficients through Einstein equation and Green-Kubo formula. It has been found that simulation results are in good agreement with experimental data for liquid argon which is taken as exponential-six fluid. The effects of density, temperature and steepness factor for repulsive part of exponential-six potential on self-diffusion coefficients are also investigated. The simulation results indicate that the self-diffusion coefficient of exponential-six fluid increases as temperature increases and density decreases. In addition, the larger self-diffusion coefficients are obtained as the steepness factor increases at the same temperature and density condition.