Using first principles calculations within density functional theory, we investigate multiphase property and phase transition of monolayer MoS2. All the quantities are calculated using the Vienna ab initio simulation package. Calculations are performed within the generalized gradient approximation with van der Waals corrections (optimized Perdew- Burke-Ernzerhof-vdW). The cutoff energy of plane-wave is set to be 400 eV. The atomic plane and its neighboring image are separated by a 15 vacuum layer. The k-meshes for the structure relaxation and post analysis are 11111 and 19191 respectively.Firstly, we obtain the geometry configurations of 2H-MoS2, 1T-MoS2 and ZT-MoS2 phases through structure relaxing. The lattice constants of 2H-MoS2 are a = 3.190 and b= 5.524 , and total energy is -39.83 eV which means that it is the most stable phase. The lattice constants of 1T-MoS2 are a = 3.191 and b = 5.528 , and total energy is -38.21 eV, which means that it is the most unstable phase. Both 2H-MoS2 and 1T-MoS2 have a three-layer structure with two S layers sandwiching one Mo layer. The difference of 1T-MoS2 from the 2H-MoS2 is the upper S layer shifting. The ZT-MoS2 derives from 1T-MoS2 through lattice distortion. The lattice constants of ZT-MoS2 are a = 3.185 and b = 5.725 , and total energy is -38.80 eV. The total energy determines the following stability order of three phases: 2H-MoS2 ZT-MoS2 1T-MoS2. Our computed results agree well with the other computed and experimental results. Band structure and density of states confirm that 1T-MoS2 is metallic and ZT-MoS2 is semiconducting. But the bandgap of ZT-MoS2 phase is only 0.01 eV. Then we compute the intrinsic carrier mobility values of 2H-MoS2 and ZT-MoS2 at 300 K with the deformation potential theory. The carrier mobility of 2H-MoS2 is between 100 cm2 V-1 s-1 and 400 cm2V-1s-1. Owing to ZT-MoS2 carrier effective mass decreasing obviously, the carrier mobility of ZT phase rises to 104 cm2V-1s-1. The great carrier mobility of ZT-MoS2 covers the shortage of 2H-MoS2 and expands the applications of monolayer MoS2.After obtaining the intrinsic properties of three phases, we investigate the phase transition of monolayer MoS2. Adsorption energy becomes more accurate with van der Waals corrections. Through comparing the adsorption energy, we conclude that the stabilities of Li absorbed on the surfaces of three phases are in the following order: 1T-MoS2 ZTMoS 2 2H-MoS2, which is opposite to the stability order of the three phases. It means that 1T-MoS2 absorbs Li more easily than 2H-MoS2. Finally we compute the energy pathways of the phase transition from 2H-MoS2 to 1T-MoS2. Introducing an electron makes the energy barrier of 2H-1T transition change from 1.85 eV to 1.49 eV. Increasing electron concentration reduces the difficulty in producing phase transition. Li intercalation plays the same role as an electron and the energy barrier drops to 1.24 eV. In conclusion, the MoS2 electron concentration change is the key reason for phase transition. The study results may provide guidance for the preparation and characterization of monolayer MoS2.