Strong shear localization effects are observed in large amplitude oscillatory shear (LAOS) simulations of a particulate suspension. Here, the structural response of this complex fluid is completely viscous and governed by the general shear-driven diffusion model by Phillips et al. [Phys. Fluids 4, 30 (1992)10.1063/1.858498]. When coupled to oscillatory shear in LAOS, this model is shown to produce concentration gradients, which imply the existence of regions of disparate viscosities across the simulated measurement gap. This suggests the presence of strong shear localization which is conceived even though the intrinsic flow curve of the model is monotonic, and the simulated geometry is a planar Couette setup, expected to display simple shear flow characteristics. This shear localization is generated due to the oscillatory shear at the shearing plate, which, therefore, induces accelerating motion. The subsequent inertial effects act as perturbations in the nonlinear response of the fluid structure to shear and are sufficient to trigger significant localization in the flow. Due to the ubiquitous nature of shear-driven diffusive mechanisms in complex fluids, these results suggest shear localization to be an integral feature of a LAOS measurement of many complex fluids.