The purpose of this study is to give a Taylor polynomial approximation for the solution of second order linear partial differential equations with two variables and variable coefficients. For this purpose, Taylor matrix method for the approximate solution of second order linear partial differential equations with specified associated conditions in terms of Taylor polynomials about any point. The method is based oil, first, taking truncated Taylor 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 Taylor coefficients. Hence, the result matrix equation can be solved and the unknown Taylor coefficients can be found approximately. (C) 2003 Published by Elsevier Inc.