An equation for the self-diffusion coefficient in a polyatomic fluid is presented as a sum of three friction coefficient terms: the temperature-dependent hard-sphere contribution, the chain contribution and the soft contribution. This equation has been developed by using the molecular dynamics simulation data for the HS chain fluid and the expression for the Lennard-Jones (LJ) fluid proposed by Ruckenstein and Liu. The real nonspherical compounds are modeled as chains of tangent LJ segments. The segment diameter sigma(LJ), segment-segment interaction energy epsilon(LJ) and chain length N (the number of segments) are obtained from the experimental diffusion data. The equation reproduces the experimental self-diffusion coefficients with an average absolute deviation (AAD) of 3.72% for 22 polyatomic compounds (1081 data points) over wide ranges of temperature and pressure. The results have been compared with that of the rough LJ (RLJ) equation. To minimize the number of the fitting parameters, the energy parameter epsilon(LJ) is estimated using a correlation obtained from viscosity data. The equation with two parameters gives an AAD of 4.72%.