: In this thesis, the spectral collocation method based on Laguerre-Gauss interpolation is investigated for solving initial value problems The outline of this thesis is as follows. In chapter one, spectral methods are reviewed and some basic concepts, which are used in the next chapters, are given. In chapter two, Laguerre collocation method are surveyed for solving ODEs. The error estimate in the and the aces is done and spectral accuracy of Laguerre collocation method will be shown. In chapter three, to show the efficiency of the method, stiff differential equations and Volterra integral equations are reviewed. Then implementation of the proposed method is studied to solve such equations. Also, application of this method for solving PDEs with initial-boundary conditions is proposed. In chapter two and three, numerical results demonstrate the efficiency and spectral accuracy of this method.