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.
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