We obtain the energy eigenvalues and wave functions of the single layer molybdenum disulfide by using an effective Hamiltonian. Moreover, the density of states and high electron-electron screening length up to 108 cm-1 are also evaluated based on the dielectric function of MoS2. It is shown that the quasi-linear energy bands split off due to the spin-orbit couplings. Plasmons in such a system are investigated theoretically within diagrammatic self-consistent field theory. In the random phase approximation, it is found that two plasma spectra can be produced via intra band transitions induced in conduction bands in monolayer MoS2 because of splitting off. The plasma spectrum frequency increases with increasing wave-vector q and electron density. It is found that the two plasmon modes induced by the spin intra-subband transitions are acoustic-like and depend strongly on wave-vector q. We find that the plasma spectrum is very different from those of graphene and two-dimensional electron gas due to the quasi-linear dispersion and spin-orbit couplings in single layer MoS2. Moreover, the plasmon frequency can be effectively controlled through changing the doping electron density. Our results exhibit some interesting features which can be utilized to realize the plasmonic devices based on the single layer MoS2.