The realization of fractional Chern insulators opens the possibility of exploring fractionally charged excitations1,2,3,4,5,6,7 and anyonic statistics8,9,10,11 in the absence of a magnetic field. A central question is whether lattice-based systems can give rise to radically new states, distinct from those observed in traditional fractional quantum Hall systems12,13,14,15,16,17,18,19,20. Here we investigate a type of moiré flat-band system composed of Bernal bilayer graphene and rhombohedral tetralayer graphene. We discover an unprecedented richness of quantum anomalous Hall insulators with Chern numbers from |C| = 1 to |C| = 7 at a moiré filling factor v = 1 and around v = 3. Remarkably, we observe an exotic fractional Chern insulator with C = 7/3 around v = 2/3, which is beyond all known fractional Chern insulators described by either the Jain sequence or current high-Chern theory21,22, 1 fractional Chern insulators. Phys. Rev. B 87, 205137 (2013)." href="#ref-CR23" id="ref-link-section-d14004720e577_2">23,24,25,26,27. Our work expands the understanding of fractionally charged excitations beyond the Landau-level basis and offers a moiré platform for exploring anyons.