In this article, we present a computationally efficient technique based on the method of Chebyshev wavelets and collocation technique for the solution of linear and nonlinear the Advection partial differential equations. We transform these problems into a system of algebraic equations using truncated Chebyshev wavelet expansions and then simplified using a suitable method. The suggested Chebyshev wavelet approach is worked out for the convergence analysis it is demonstrated that the estimation of a function using Chebyshev wavelets converges uniformly to itself. It is also anticipated that the proposed approach would be more efficient and suitable for solving a variety of nonlinear partial differential equations that occur in science and engineering. Examples are given to show how the suggested wavelet method provides enhanced accuracy for a wide range of problems.