In this paper, we present a numerical solution method which is based on Taylor Matrix Method to give approximate solution of the Bagley-Torvik equation. Given method is transformed the Bagley-Torvik equation into a system of algebraic equations. This algebraic equations are solved through by assistance of Maple 13. Then, we have coefficients of the generalized Taylor series. So, we obtain the approximate solution with terms of the generalized Taylor series. Further some numerical examples are given to illustrate and establish the accuracy and reliability of the proposed algorithm.