Mutual diffusion coefficients can be successfully predicted with models based on the Darken equation. However, Darken-based models require composition-dependent self-diffusion coefficients which are rarely available. In this work, we present a predictive model for composition-dependent self-diffusion coefficients (also called tracer diffusion coefficients or intradiffusion coefficients) in nonideal binary liquid mixtures. The model is derived from molecular dynamics simulation data of Lennard-Jones systems. A strong correlation between nonideal diffusion effects and the thermodynamic factor is observed. We extend the model by McCarty and Mason (Phys. Fluids 1960, 3, 908-922) for ideal binary gas mixtures to predict the composition-dependent self-diffusion coefficients in nonideal binary liquid mixtures. Our new model is a function of the thermodynamic factor, the self-diffusion coefficients at infinite dilution, and the self-diffusion coefficients of the pure substances, which are readily available. We validate our model with experimental data of 9 systems. For both Lennard-Jones systems and experimental data, the accuracy of the predicted self-diffusion coefficients is improved by a factor of 2 compared to the correlation of McCarty and Mason. Thus, our new model significantly expands the practical applicability of Darken-based models for the prediction of mutual diffusion coefficients.