Self-and binary Maxwell-Stefan diffusion coefficients were determined by equilibrium molecular dynamics simulations with the Green-Kubo method. This study covers selfdiffusion coefficients at liquid states for eight pure fluids, i.e. F 2 , N 2 , CO 2 , CS 2 , C 2 H 6 , C 2 H 4 , C 2 H 2 and SF 6 as well as Maxwell-Stefan diffusion coefficients for three binary mixtures N 2 +CO 2 , N 2 +C 2 H 6 and CO 2 +C 2 H 6 . The fluids were modeled by the two-center Lennard-Jones plus point-quadrupole pair potential, with parameters taken from previous work of our group which were determined solely on the basis of vapor-liquid equilibrium data. Self-diffusion coefficients are predicted with a statistical uncertainty less than 1% and they agree within 2% to 28% with the experimental data. The correction of the simulation data due to the finite size of the system increases the value of the self-diffusion coefficient typically by 10%. If this correction is considered, better agreement with the experimental data can be expected for most of the studied fluids. Maxwell-Stefan diffusion coefficients for three binary mixtures were also predicted, their statistical uncertainty is about 10%. These results were used to test three empirical equations to estimate Maxwell-