In this work, the stopping power due to free and bound electrons in a plasma target is analyzed for two different kinds of projectile, protons and alpha particles. The stopping of free electrons is calculated using the dielectric formalism, well described in previous literature. In the case of bound electrons, Hartree-Fock methods and oscillator strength functions are used. The ionization degree of the plasma target is calculated using the Saha equation. Differences between the two methods of calculations for bound electrons are shown in noble gases. The influence of ionization is also estimated for argon plasma. Finally, we compare our calculations with two experiments. In the first one the stopping is calculated for protons in polyethylene plasma, and the second one the stopping is obtained for alpha particles in hydrogen plasma. In both cases, a good agreement with the experimental data is found.