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In this paper, a new set of high-order FDTD schemes are introduced using the symplectic Runge-Kutta-Nystrom integration techniques for Hamilton system. This method disperses the Maxwell functions in the time domain based on symplectic method, which can preserve the exchangeability of the Hamilton system for phase space and the total energy. Central differences are maintained in the approximation of spatial derivatives. Numerical results suggest that the SRKN FDTD algorithm acquires better stability and accuracy compared with the conventional high order FDTD schemes and Symplectic Runge-Kutta FDTD.