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 3-orbitals model, we reveal a spin triplet pairing in doped MoS₂ by employing the finite temperature determinant quantum Monte-Carlo approach. In a wide filling region of <n>=0.8~1.0, the fn-wave pairing dominates over other symmetries, and as the filling is lower than <n>=0.8, the f-wave tends to be dominated. The pairing susceptibility strongly increase as the on-site Coulomb interaction increases while it is insensitively to the spin-orbit coupling. The observed dependences of the pairing susceptibility on electron fillings and spin-orbit couplings are illustrated with the changes of Fermi surface topologies.