  The integer quantum Hall state occurs when the Landau levels are fully
occupied by the fermions, while the fractional quantum Hall state usually
emerges when the Landau level is partially filled by the strongly correlated
fermions or bosons. Here, we report two fractional Chern insulating states of
the hard-core bosons in a multi-band lattice model hosting topological flat
bands with high Chern number. The previously proposed $\nu=1/3$ fractional
Chern insulating state inherited from the high Chern number $C=2$ of the lowest
topological flat band is revisited by the infinite density matrix
renormalization group algorithm. In particular, we numerically identify a
bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer
fillings. We show two lower topological flat bands jointly generate an
effective $C=1$ Chern band with half-filling. Furthermore, we find a strictly
particle-hole-like symmetry between the $\nu$ and $3-\nu$ filling in our model.
These findings extend our understanding of quantum Hall states and offer a new
route to realize the novel fractional states in the system with multi-bands and
high-Chern numbers.
