Abstarct: Dense plasma by a combination of ions and degenerate positrons and electrons are to be known as a quantum plasma. Plasmas in this type of light particles like electrons and positrons at high density and temperature relatively low can be degenerate. Quantum effects become important when the thermal wavelength de-Brogile is small then average distance particles or when the system temperature same with the Fermi temperature. Recently, due to extremely low temperatures and also the interest to study the nanoscale, quantum properties of the plasma is increased. whereas density of this plasma are comparable to the density of solids and there have temperatures of a few electron volts, they can be a subset of the physics of condensed matter and described phenomena such as cool and tunneling phenomena, quantum diodes, lasers-solid ,etc by them. so study quantum plasma will be necessary. In this study, we peruse the behavior of linear and nonlinear quantum plasma in a small interval. First we set the range of temperature and density that quantum effects will be felt and whereas the classical plasma models describing quantum plasma behavior will not be able to explain, to describe these plasmas provide new models. Plasma behavior is consistent in the ways of solving their issues to consider as a model to describe plasma. For linear plasma effects, such as the linear dispersion relation of waves excited in the use of linear theory. Linear theory is baxsed on the approximation of small amplitude waves. In this range, we ignored of all second-and higher-order nonlinear terms and their derivatives. According to this theory, any physical disorder in the system, periodic and behave independently, and the propagation of waves is shown with linear dispersion relation .We mean the effects of nonlinear behavior of the plasma using the linear theory is justified. When these behaviors are basically of large amplitude waves can appear. Other factors such as the Landao damping phenomenon also involved in the plasma nonlinear behavior. The solitary waves or Solitons are most important solutions of nonlinear equations are solved these plasmas.