In this article, we derive a new numerical method to solve fractional differential equations containing Caputo-Fabrizio derivatives. The fundamental concepts of fractional calculus, numerical analysis, and fixed point theory form the basis of this study. Along with the derivation of the algorithm of the proposed method, error and stability analyses are performed briefly. To explore the validity and effectiveness of the proposed method, several examples are simulated, and the new solutions are compared with the outputs of the previously published two-step Adams-Bashforth method.