In this paper, we present Chebyshev spectral collocation method to the solve linear partial differential
equations (PDEs) with variable coefficients subject to a given initial and boundary conditions. First,
we introduce an approximation to the unknown function and its derivatives by using Chebyshev differentiation matrices. Secondly, the operational matrix of differentiation and Chebyshev polynomials
are used to convert our problem to a system of linear equations. Finally, the effectiveness of the
method is illustrated in numerical experiment such as Poisson equation.