  Searching for triplet superconductivity has been pursued intensively in a
broad field of material science and quantum information for decades.
Nevertheless, these novel states remain rare. Within a simplified effective
three-orbital model, we reveal a spin triplet pairing in doped MoS$_2$ by
employing both the finite temperature determinant quantum Monte Carlo approach
and the ground state constrained-phase quantum Monte Carlo method. In a wide
filling region of $\avg{n}=0.60-0.80$ around charge neutrality $\avg{n}=2/3$,
the $f$-wave pairing dominates over other symmetries. The pairing
susceptibility strongly increases as the on-site Coulomb interaction increases,
and it is insensitive to spin-orbit coupling.
