Enhanced third-harmonic generation in a one-dimensional photonic crystal doped with third-order nonlinear medium was numerically investigated using the multiple-scale method and the split-step Fourier transform. The optimal fundamental frequency for third-harmonic wave generation was determined from the transmission spectrum. The third-harmonic pulse intensities grow, depending on the structure thickness and the fundamental-frequency detuning parameter, which determines the band-edge phase matching condition. Furthermore, the total energy output of third-harmonic pulses, depending on the fundamental-frequency pulse width, may be more than 1000 times the energy produced by a phase-matched bulk medium. A narrow pulse with bandwidth less than the band-edge transmission peak enables high conversion efficiency. The maximum conversion efficiency of the forward component may be 12 to 13 orders of magnitude greater than that of the backward component.