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We present a systematic study of the self-diffusion coefficient for a fluid of particles interacting via the square-well pair potential by means of molecular dynamics simulations in the canonical (N,V,T) ensemble. The discrete nature of the interaction potential is modeled through the constant force approximation and the self-diffusion coefficients is determined for several packing fractions at super critical thermodynamic states. The dependence of the self-diffusion coefficient with the potential range $\lambda$ is analyzed in the range of $1.1 \leq \lambda \leq 1.5 $. The obtained molecular dynamics simulations results are in agreement with the self-diffusion coefficient predicted with the Enskog method. Additionally, we soh that the diffusion coefficient is very sensitive to the potential range, $\lambda$, at low densities leading to a density dependence of this coefficient not shared with other macroscopic properties such as the equation of state. The constant force approximation used in this work to model the discrete pair potential has shown to be an excellent scheme to compute the transport properties using standar computer simulations. Finally, the simulation results presented here are resourceful to improving theoretical approaches, such as the Enskog method.