Analysis of non-Newtonian fluids displacement by Newtonian fluids is one of the most important issues in mechanical engineering because of its economical importance and broad application in the oil and gas industry, drilling, petrochemical and meteorological phenomena. Numerical simulation of this problem will be very difficult if fluids in solution domain are considered immiscible; because there is complex dynamics at the interface of them. In recent years, few studies have concentrated on CFD methods for the modeling of this type of displacement. These researches have not provided accurate and comprehensive results due to significant simplifications and considerable limitations. According to said reasons and because of special features of the lattice Boltzmann method, such as automatic separation of phases, less computational burden, easier coding, local computation of shear rate etc., this method is used for this research. based on lattice Boltzmann method, there are several multi-phase models that generally are categorized in three groups, named the free energy, the Shan-Chen and the color gradient. The simulations in this study are done by means of a developed procedure of Shan-Chen model which is named the He-Chen model. to evaluate the accuracy of numerical results the Laplace, the turning square bubbles to circular ones, the droplets sticking, the Rayleigh-Taylor instability, the Kelvin-Helmholtz instability and the automatic separation of phases tests are used. Introducing six models of non-Newtonian viscosity structure (the Bingham, the Herschel bulky, the Carreau, the Carreau-Yasuda, the cross and the power law) and by using the He-Chen model of multicomponent lattice Boltzmann method, displacement of non-Newtonian fluids by Newtonian ones is simulated and the results are shown trough eleven types of figures. These figures show the type of injected fluid movement in the secondary fluid and displacement efficiencies according to various definitions which have been presented for them. Finally it is found that the parameters in viscosity determination function can have considerable effects on the nature of flow by creating slimy resisting force against invading fluid movement. Keywords: Lattice Boltzmann method, multicomponent flow, He-Chen model, Newtonian displacement flow, non-Newtonian displacement flow