Two kinds of special long-period fiber gratings, phase-shift and apodised long-period gratings, were studied by many researchers, because of their special spectral characteristics. According to the theory of long-period moiré gratings, with the methods of step-by-step ultraviolet (UV) writing and double-exposure with different grating period, several kinds of long-period moiré gratings were fabricated in the hydrogened high-germanium-doped fiber by controlling the period and the first position of both exposure and the exposure-time of each step, which realized the effects of phase-shift and apodization. The results indicated that the moiré gratings technology can be well applied in fabricating the special kinds of long-period fiber gratings, such as phase-shifted and apodised gratings.