Herein,an approach known as conformable double Laplace decomposition method (CDLDM) is suggested for solving system of non-linear conformable fractional differential equations.The devised scheme is the combination of the conformable double Laplace transform method (CDLTM) and,the Adomian decomposition method (ADM).Obtained results from mathematical experiments are in full agreement with the results obtained by other methods.Furthermore,according to the results obtained we can conclude that the proposed method is efficient,reliable and easy to be implemented on related many problems in real-life science and engineering.