We report the inscription of low-loss fiber Bragg gratings using focused femtosecond (fs) pulses and a continuous core-scanning technique. This direct-write technique produces high-fidelity Type I-IR gratings that share the inherent advantages of other direct-write methods, such as the point-by-point (PbP) method, for which the grating period is a free parameter. However, here we demonstrate an order of magnitude improvement in scattering loss compared to PbP gratings, to a level comparable with that of phase-mask-based fs inscription. A first-order grating was inscribed in standard telecommunications fiber with -49 dB transmission at the Bragg wavelength and 0.1 dB broadband scattering loss. Potential application of these gratings to large-mode-area fibers and chirped grating fabrication are highlighted.