Abstract: The present presentation aims at investigating the collisional energy loss for a heavy fermion in quantum-relativistic plasmas. In the weakly-coupled gauge plasma, the perturbative thermal field theory can be used to describe well the properties of plasma and extensively applied in the calculation of dynamical quantities such as energy loss. In this method, the screening effects and the collective behavior of the plasma are computed consistently using resummation of hard thermal loops according to the Braaten-Pisarski method. The main approach in this research is to develop the calculation of heavy fermion energy loss in equilibrium plasmas to non-equilibrium ones. In this regard, the method of calculating the energy loss of heavy fermions in equilibrium plasmas provided by Braaten and Thoma in imaginary time formalism of thermal field theory is presented. By extending the above method to the case of real time formalism, distribution functions appear explicitly in the energy loss phrase. Therefore by replacing the non-equilibrium distributions, energy loss for a heavy fermion in non-equilibrium gauge plasmas is calculated. Following as two examples of the energy loss calculations in non-equilibrium quantum-relativistic plasmas, the energy loss of a muon in the nonthermal EPP and the energy loss of a heavy quark in the QGP at finite chemical potential is investigated. Finally, by simulating the system with the nonthermal muon beam passing through a hot and dense equilibrium EPP, the effects of the nonthermal parameter of the beam particles distribution on the energy exchange and the evolution of the plasma-beam system is studied.