The design of a complex phase mask (CPM) for inscribing multi-notch fiber Bragg grating filters in optical fibers for OH suppression in astronomy is presented. We demonstrate the steps involved in the design of a complex mask with discrete phase steps, following a detailed analysis of fabrication constraints. The phase and amplitude of the complex grating is derived through inverse modelling from the desired aperiodic filter spectrum, following which the phase alone is encoded into the surface relief of a CPM. Compared to a complicated “running-light” Talbot interferometer based inscription setup where the phase of the inscribing beam is controlled by electro- or acousto-optic modulators and synchronized to a moving fiber translation stage, CPM offers the well-known convenience and reproducibility of the standard phase mask inscription technique. We have fabricated a CPM that can suppress 37 sky emission lines between 1508 nm to 1593 nm, with a potential of increasing to 99 channels for suppressing near-infrared (NIR) OH-emission lines generated in the upper atmosphere and improving the performance of ground-based astronomical telescopes.