In this paper, a new method based on the Chebyshev wavelet expansion is proposed for solving a coupled system of nonlinear ordinary differential equations to model the unsteady flow of a nanofluid squeezing between two parallel plates. Chebyshev wavelet method is applied to compute the numerical solution of coupled system of nonlinear ordinary differential equations in order to model squeezing unsteady nanofluid flow. The approximate solutions of nonlinear ordinary differential equations thus obtained by Chebyshev wavelet method are compared with those of obtained by Adomian decomposition method (ADM), fourth order Runge-Kutta method and homotopy analysis method (HAM). The results obtained by the above methods are illustrated graphically and are discussed in details. The present scheme is very simple, effective and appropriate for obtaining numerical solution of squeezing unsteady nanofluid flow between parallel plates. (C) 2015 Elsevier B.V. All rights reserved.