A plasma with two different particle types and at different temperatures has been considered, so that each type of ion with MaxwellBoltzmann distribution function is in temperature equilibrium with itself. Using the extracted nuclear elastic scattering differential cross-section from experimental data, solving the Boltzmann equation, and also taking into account the mobility of the background particles, temperature equilibration rate between two different ions in a fusion plasma is calculated. The results show that, at higher temperature differences, effect of nuclear elastic scattering is more important in calculating the temperature equilibration rate. The obtained expressions have general form so that they are applicable to each type of particle for background (𝑏) and each type for projectile (𝑝). In this paper, for example, an equimolar Deuterium-Hydrogen plasma with density 𝑛 = 5 × 1025 cm−3 is chosen in which the deuteron is the background particle with temperature (also electron temperature) 𝑇𝑏 = 1 keV (usual conditions for a fusion plasma at the ignition instant) and the proton is the projectile with temperature 𝑇𝑝 > 𝑇𝑏. These calculations, particularly, are very important for ion fast ignition in inertial confinement fusion concept
