This paper presents a semianalytical method, the modified multistep differential transform method (MMSDTM), for solving linear and nonlinear fractional-order differential equations with the order between 0 and 2. This method can be considered as a variant of the predictor-corrector method (PCM). The multistep differential transform method (MSDTM), which does not take the memory effect into account and yields unsatisfactory solution very rapidly, is first used to find an estimation as the predictor of the solution. In the corrector procedure, the memory term associated with the fractional-order derivative is decomposed by the subtraction of two integrals; one is abnormal with singularity and the other is normal without singularity and the two integrals are calculated by using the MSDTM and a simple numerical scheme, respectively. Four illustrative examples are given to show that the MMSDTM requires much less computational cost and retains high computational accuracy, compared with the widely used PCM.