A sparse-array metasurface (MTS) antenna corresponds to a continuously modulated sheet impedance on top of a grounded slab, periodically repeated over many unit cells (with a few wavelengths cell size). The structure is fed with an array of surface-wave (SW) feeds placed at the center of each cell. The modulated MTS is designed to generate a sharp embedded element radiation pattern (EEP) able to filter out possible grating lobes that may appear due to the large size of the unit cell (as compared to the classically adopted half-wavelength size in traditional phased arrays). This paper proposes a Method of Moments (MoM) tool developed to efficiently analyze modulated MTSs with periodic boundary conditions (PBC). Such structures may be used to provide continuous beam scanning with a sparse feeding network. In this letter, the unknown current distribution as well as the sheet impedance are expanded into a set of regularly spaced Gaussian basis functions. The adopted Gaussian functions along with the mesh regularity are employed to dramatically accelerate the computation of the MoM matrix with FFT-based accelerations. The numerical results are validated with that from the commercial software HFSS.