We theoretically investigate the Cooper-pair symmetry that can be realized in hole-doped monolayer MoS2 by solving linearized BCS gap equations in the three-orbital attractive Hubbard-like model in the presence of the atomic spin-orbit coupling. In hole-doped monolayer MoS2, both spin-orbit coupling and the multiorbital effects are more prominent than those of an electron-doped system. Near the valence band edge, the Fermi surfaces are composed of three different types of hole pockets; namely, one consists mainly of the almost spin degenerate |dz2) orbital near the Γ point, and the others are the spin-split upper and lower bands near the K and K′ points arising from the |dx2-y2) and |dxy) orbitals. The number of relevant Fermi pockets increases with the increase of the doping. At very low doping, the upper split bands of |dx2-y2) and |dxy) are concerned, yielding extremely low Tc due to the small density of states of the split bands. For further doping, the conventional spin-singlet state (SS) appears in the Γ pocket, which has a mixture of the spin-triplet, orbital-singlet (ST-OS) and spin-singlet, orbital-triplet (SS-OT) states in the K and K′ pockets. The ratio of the mixture depends on the relative strength of the interactions and the sign of the exchange interactions. Moderately strong ferromagnetic exchange interactions even lead to the pairing state with the dominant ST-OS state over the conventional SS one. With these observations, we expect that the fascinating pairing with relatively high Tc emerges at high doping that involves all three Fermi pockets.