This paper analyzes the 2-point Fractional Block Method based on the Backward Differentiation Formula for solving stiff fractional-order differential equations. An analysis of the stability properties of the method is conducted to verify its A-stability. Since the method fulfills the characteristic, it can be employed to approximate solutions for stiff problems. Consequently, two test problems are solved to assess the method’s performance. As a result, the derived method exhibits advantages over existing methods in terms of accuracy.