In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problemneeds to have an analytic solution. Sowe investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numericalmethods to showthe performance and good accuracy of themethods. The numerical orders of convergence show that the method has exponential rate of convergence.