Human capabilities in manipulating many different tools with dexterity suggest modular neural organization at functional levels, but anatomical modularity underlying the capabilities has yet to be demonstrated. Although modularity in phylogenetically older parts of the cerebellum is well known, comparable modularity in the lateral cerebellum for cognitive functions remains unknown. We investigated these issues by functional MRI (fMRI) based on our previous findings of a cerebellar internal model of a tool. After subjects intensively learned to manipulate two novel tools (the rotated mouse whose cursor appeared at a rotated position, and the velocity mouse whose cursor velocity was proportional to the mouse position), they could easily switch between the two. The lateral and posterior cerebellar activities for the two different tools were spatially segregated, and their overlaps were <10%, even at low statistical thresholds. Activities of the rotated mouse were more anterior and lateral than the velocity mouse activities. These results were consistent with predictions by the MOdular Selection And Identification Controller (MOSAIC) model that multiple internal models compete to partition sensory-motor experiences and their outputs are linearly combined for a particular context.