We have studied in this paper, investigated the influence of an electron beam on a dense warm inhomogeneous plasma, and the instability resulting in this system, through studying of the influence of plasma density variation on the beam-plasma instability growth. Where we considered the plasma density is in the same order of Fermi gas, and we considered the model of homogeneous cold beam-inhomogeneous warm plasma system, with small phase velocity in compared with the case of existence of an external magnetic field. We derived the differential equations that describe this system in the case of collision plasma because of its high density, and we derived the differential equation that expresses the energy absorbed in the wholesale and we solved this equation then we drew the suitable graphics using Mathcad program, discussed, and analyzed the results that we reached. Results indicated an amplification of outcome waves in wholesale because of the absorbed energy and instability increasing in the system.