This letter describes the multi-rate locally implicit block leapfrog scheme (LIBLS) for the fast transient analysis of multi-layered power/ground planes. LIBLS is the numerical method constructed by applying a locally implicit scheme to the existing scheme, which is based on an explicit leapfrog scheme. The proposed method improves LIBLS with introducing a multi-rate technique in the time domain, and using different time step sizes for a variety of sub-circuits, and is applicable to the multi-layered network with many coupling elements.Index Terms-Delaunay triangular meshes, locally implicit block leapfrog scheme (LIBLS), multi-layer power/ground planes, multi-rate, time-domain analysis, Voronoi tessellation.