Energy loss due to a fast-electron beam interacting with the hot plasma at a high density is analysed theoretically.By splitting the particle density fluctuations into the individual part due to the random thermal motion of the individual electrons and the collective part due to plasma-wave excitation, we are conceed with the collective interaction of the relativistic plasma electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the "Debye length" with the modification of the relativistic effect. And finally we calculate the energy loss of a fast-electron beam due to the excitation of collective oscillation in the hot plasma.