Abstarct: Many problems arising in the field of sciences and engineering can be modeled by differential equations which because of the lack of appropriate mathematical methods, most of the analytical solutions are challenging to acquire. Therefore, approximation and numerical techniques should be used. In this thesis, we apply Chebyshev-Legendre collocation method for solving Burgers-Fisher and Viscous-Burgers equations which are partial differential and system of linear differential equations respectively. This technique is used to convert the problems to the solution of linear or nonlinear algebraic equations via applying Chebyshev and Legendre functions with collocation points. We compare these solutions with exact results and show that it is accurate.