A new design of a passive optical fiber waveguide with a large mode area (LMA) and strong stimulated Brillouin scattering (SBS) suppression is proposed. The fiber core consists of two parts: a central one, doped with Al2O3 and GeO2, and a peripheral one, doped with P2O5 and F. The doping profiles form a gradient-increasing profile of the acoustic refractive index, which effectively implements the acoustic multimode SBS suppression method. Measurements of the SBS gain spectrum and SBS threshold power were carried out, showing an increase in the SBS threshold of no less than 11 dB compared to a conventional uniformly doped passive LMA fiber.