In this paper, a new method based on combination of the natural transform method (NTM), Adomian decomposition method (ADM), and coefficient perturbation method (CPM) which is called “perturbed decomposition natural transform method” (PDNTM) is implemented for solving fractional pantograph delay differential equations with nonconstant coefficients. The fractional derivative is regarded in Caputo sense. Numerical evaluations are included to demonstrate the validity and applicability of this technique.