This paper is devoted to propose the numerical solution pantograph differential equations via a new computational approach of Hermite collocation method. The convergence of the Hermite collocation method is investigated. The numerical solution of pantograph differential equations is obtained in terms of Hermite polynomial. Nonlinear pantograph differential equations are solved and compared with the exact solutions to show the validity, applicability, acceptability and accuracy of the Hermite collocation method. The approximated results show good agreement with the exact solutions, hence indicate good performance of the methods in solving the corresponding equations.