The symplectic integrator (SI), widely used in quantum and classical physics, as a stable and reliable numerical method, was applied to solve the time-dependent Maxwell equations. By employing a wave number space in evaluating space-derivatives, we can avoid numerical errors inherent to finite difference approximations to differential operators. We derived the stability condition and numerical dispersion formula for the studied FFT based SI scheme. A comparison to the conventional finite-difference time-domain method was also made.