  Moir{\'e} superlattice realized in two-dimensional heterostructures offers an
exciting platform to access strongly-correlated electronic states. In this
work, we study transition metal dichalcogenides (TMD) Moir{\'e} superlattices
with time-reversal-symmetry and nontrivial spin{/valley}-Chern numbers.
Utilizing realistic material parameters and the method of exact
diagonalization, we find that at a certain twisting angle and fractional
filling, gapped fractional topological states, i.e., fractional Chern
insulators, are naturally {stabilized} by simply introducing the Coulomb
repulsion. In contrast to fractional quantum Hall systems, where the
time-reversal symmetry has to be broken explicitly, these fractional states
break the time-reversal symmetry spontaneously. {We show that the Chern number
contrasting in the opposite valleys imposes a strong constraint on the nature
of fractional Chern insulator and the associated low energy excitations.} We
also propose to realize the non-abelian Moore-Read state in TMD Moir{\'e}
superlattice sandwiched between nonlinear dielectric media.
