A model is suggested describing the effect of grain boundary (GB) sliding on the fracture toughness of ceramic/graphene composites. Within the model, GB sliding near the tip of a large mode I crack initiates the formation of a new nano- or microcrack at an adjacent GB. The new crack merges with the pre-existent one, thus providing crack propagation. For the situation where the suggested crack growth mechanism restricts the fracture toughness of ceramic/graphene composites, we calculated the dependence of the fracture toughness on grain size and lateral dimensions of graphene platelets. The calculations demonstrated that GB-sliding-assisted crack growth reduces fracture toughness, and the effect is strongest for the case where grain size is small and the lateral graphene platelet dimensions are close to the sizes of GBs. The results of the calculations agree with the experimental data on the fracture toughness of alumina/graphene composites.