The moire superlattice of misaligned atomic bilayers paves the way for designing a new class of materials with wide tunability. In this work, we propose a photonic analog of the moire superlattice based on dielectric resonator quasi-atoms. In sharp contrast to van der Waals materials with weak interlayer coupling, we realize the strong coupling regime in a moire superlattice, characterized by cascades of robust flat bands at large twist angles. Surprisingly, we find that these flat bands are characterized by a non-trivial band topology, the origin of which is the moire pattern of the resonator arrangement. The physical manifestation of the flat band topology is a robust one-dimensional conducting channel on the edge, protected by the reflection symmetry of the moire superlattice. By explicitly breaking the underlying reflection symmetry on the boundary terminations, we show that the first-order topological edge modes naturally deform into higher-order topological corner modes. Our work pioneers the physics of the moire superlattice beyond the weakly coupled regime and introduces a designable platform to control photonic topological insulator phases using moire patterns.