The objective of this research has been devoted to solve linear fuzzy fractional differential equations (FFDEs) of the Caputo sense. The basic idea is to develop a fractional linear multistep method for solving linear FFDEs under fuzzy fractional generalized differentiability. For safely illustrating the advantages and potential of the presented method, a comparison with the fractional Euler method has to be analyzed in depth. We are interested in using a simple method to obtain gripping results.