The major goal of this paper is to find accurate solutions for linear fractional differential equations of order \(1 < \alpha < 2\) . Hence, it is necessary to carry out this goal by preparing a new method called Fractional Finite Difference Method (FFDM). However, this method depends on several important topics and definitions such as Caputo's definition as a definition of fractional derivative, Finite Difference Formulas in three types (Forward, Central and Backward) for approximating the second and third derivatives and Composite Trapezoidal Rule for approximating the integral term in the Caputo's definition. In this paper, the numerical solutions of linear fractional differential equations using FFDM will be discussed and illustrated. The purposed problem is to construct a method to find accurate approximate solutions for linear fractional differential equations. The efficiency of FFDM will be illustrated by solving some problems of linear fractional differential equations of order \(1 < \alpha< 2\).