A new self-diffusion coefficient equation is derived for pure Lennard-Jones (LJ) model fluid based on the molecular dynamics (MD) simulation data in literatures, which could be applied to gas, liquid and supercritical fluid (0 less than or equal to n* less than or equal to 1.0 and 0.8 less than or equal to T* less than or equal to 4.0) with total AAD of 4.95%. With a generalized expression for the LJ parameters of pure real fluids, the proposed equation is extended to apply to pure real substances. The prediction accuracy of 17 substances and 1226 data points is 18.51%. Combining with the Lorentz-Berthelot combining rule, the proposed equation is extended to the prediction of the infinite dilute binary diffusion coefficients, The total AAD for 74 kinds of solution (55 solutes. 6 solvents, total 1141 experimental data points) is 17.32%. There is no adjustable parameter in the new proposed generalized equation and with only the critical constants. the prediction accuracy is good and the equation could be used in preliminary process development and design.