Abstract: A novel difference-spectrum hybrid numerical technique is proposed in this paper. In this method, each time dependent variable in Maxwell's equations is periodically continued with proper approximation, which results in the conversion of the continuous-spectrum problem to a discrete one by virtue of the consistent of solution before and after periodical continuation in the first period. The discrete spectra of the field quantities after continuation are obtained from difference Maxwell curl equations in frequency-domain and the time-domain solution of the original problem is derived from their inverse Fourier transforms. The strong point of the proposed method is its high capability of calculating any dispersive media and utilizing PML boundary condition without additional codes. Due to its unconditional stability, this technique excels Yee's FDTD in dealing with electromagnetic problems where the characteristic sizes of the scatter are much larger than the wavelength of the stimulant source. Numerical experiments demonstrate its effectiveness, easy implementation and high precision.