Layered Li transition metal oxides are widely used as active materials for the positive electrode of Li-ion rechargeable batteries, where intercalation of Li in the metal oxide is a fundamental phenomenon that determines the performance of the batteries. The intercalation process is significantly affected by the crystal anisotropy and grain boundaries, particularly for all-solid-state thin film batteries. Therefore, to improve the batteries, a thorough understanding of the intercalation process on the nanometer length scale is essential. To this end, we have proposed phase-field models for calculating the relation between the realistic polycrystalline microstructure and the apparent Li diffusion coefficient. A crystallographic orientation was randomly allocated to each crystal grain in a two-dimensional polycrystalline microstructure. The simulation results show that the apparent Li diffusivity is sensitive to the diffusivity of the grain boundaries, the spatial distribution of the crystal orientation for each grain, and the grain size. The diffusivity of a small-grained structure is determined by the properties of the grain boundary. On the other hand, the diffusivity of a large-grained structure depends considerably on the relative orientation angle between neighboring grains, even when the Li conductivity of the grain boundary is large. (C) 2012 Elsevier B.V. All rights reserved.