A matrix method, which is called the Chebyshev‐matrix method, for the approximate solution of linear differential equations in terms of Chebyshev polynomials is presented. The method is based on first taking the truncated Chebyshev series of the functions in equation and then substituting their matrix forms into the given equation. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients. To illustrate the method, it is applied to certain linear differential equations under the given conditions and the results are compared.