Abstarct: Today, the viscoelastic fluids have plenty usages in oil, chemistry, military and medical industries. Viscoelastic fluids simultaneously show the qualities of viscous fluid and solid elastic, also due to elastic qualities of this fluids in Unsteady shear flows, they gain the unique quality like the damped oscillating behavior in velocity field without foreign oscillating factor in boundary condition and outside forces. In this essay, the power-law preconditioning method with preconditioned matrix has been used for Numerical stability of unsteady flow of viscoelastic fluid passing through two fixed parallel plates. the preconditioning matrix is adapted from the stress field power-law relation. In the power-law preconditioning method with a change in time derivation of conservation equation, the governing equations are converted from parabolic-elliptic form to hyperbolic form (artificial compressibility). For modeling these kinds of flow, simple Maxwell equation is used. To solve the governing and constituent equations, a dual-time implicit algorithm and discretization of equations with finite difference method are applied. For the convergence toward stabilization, The Vosoughifar four-step numerical method is used. The computations of viscoelastic fluids flow passing through two fixed parallel plates, are presented in Reynolds numbers, Weissenberg numbers and Viscosity ratio. The results contain velocity profile and contour, and the effect of standard compressibility methods, standard preconditioning and power-law preconditioning with pressure, velocity and stress sensor on the rate of convergence for these flows. The results are validated using numerical computations and analysis, which indicate that the locally stress sensor power-law preconditioning method for viscosity ratios less than 5% and the locally velocity sensor power-law preconditioning method for viscosity ratios equal to or greater than 5% have the highest convergence speed, thus reducing the computational cost. In addition to high accuracy, the locally method of stress sensor power-law preconditioning has high stability in numerical solution for unsteady viscoelastic fluid flow.