For a granular thin-film medium, the total noise is determined by intergranular interactions and local anisotropy fields. Among these two factors, the effect of local anisotropy on medium noise is relatively less clear. A micromagnetic model is used to study four kinds of media with different anisotropy distributions. Perpendicular anisotropy is examined in two of the four media: One has a uniform perpendicular component for all grains, the other has some perpendicular grains randomly distributed. It is found that if exchange coupling is absent, the medium with the most uniformly distributed crystalline anisotropy has the lowest noise. Otherwise, the medium with the most nonuniformly distributed anisotropy yields the lowest noise.