We investigate the influence of the variable plasma density on the spatial growth of the beam-plasma instability, considering the model of homogeneous cold beam-inhomogeneous warm plasma system under the condition of the smallness of phase velocity of waves compared to the beam velocity. We determine a direction of the beam with unmagnatized plasma. Considering a one – dimensional electrostatic oscillation when the directions of beam propagation, plasma density gradient and wave electric field coincide with X-axis. To formulate mathematical equation of beam and plasma then we make studying equation linearized, and then study the continuity equation and boundary conditions. Formulating electric field density then study a case in which a plasma is collisional because of its high density and the temperature .Finally we drive absorbent energy and find solutions of these equations then draw it.