Self-consistent calculations of the stopping power for alpha particles in hot dense Au plasmas are performed in a wide projectile energy range with a fixed density ρAu = 19.3 g cm−3 and the electron temperature range from 0.4 to 5 keV on the basis of the relativistic ion-sphere model. All the mechanisms, which have strong influences on stopping power, are discussed in detail. The distribution of the free electron velocity component is found to be much flatter than the Maxwellian distribution due to the strong electrostatic field within the ion sphere in the hot dense plasmas, which results in the suppression of the stopping mechanism by plasma polarization and close collision for a projectile energy below 1 MeV u−1. The influence of inelastic scattering is considerably weakened due to the strong neutralization from the impact excitation, ionization and their reverse processes almost in the entire energy range below 10 MeV u−1 although the contribution of each process is quite large. Nuclear stopping is found to increase with the temperature. Our calculations are compared with other models and some explanations are presented for the difference between our results and other models. The Bethe equation is found to overestimate the contribution of inelastic processes by at least 10%. Different mechanisms are found to play their role in different energy ranges and all the mechanisms should be considered in order to get reliable data of stopping power.