A new equation of self-diffusion coefficients for real fluids is proposed over wide temperature and density ranges.The new equation is derived from the molecular dynamics simulation data of LJ model fluid in literature

which could be applied to gas

liquid and supercritical fluid (0≤ ρ * ≤1.0

0.8≤ T *≤4.0) with AAD 4.95% .With a generalized expression for the LJ parameters of pure real fluids according to the corresponding state principle and critical properties

the proposed equation is extended to pure real substances with the prediction accuracy 18.83%.Correlated LJ parameters are also used for comparison and the total AAD is 3.43% for 19 pure substances and 1299 data points.The new self-diffusion equation could be used in process design and development.