As one kind of layered transition metal sulfides, Two-dimensional WS2 has attracted much attention because of its special layered structure, tunable band gap and stable physicochemical properties. Combining Boltzmann transport equation (BTE) and density functional theory (DFT), the phonon transport properties of monolayer WS2 were investigated by first-principles. The harmonic and anharmonic effects of phonons to the lattice thermal conductivity of WS2 were analyzed. The critical mean free path of phonon for WS2 was calculated, which demonstrated that the thermal conductivity of WS2 could be regulated by adjusting the frequency. The results show that the intrinsic lattice thermal conductivity of monolayer WS2 is 149.12 W/(m·K) at 300 K, and it will decrease with the increase of temperature. The acoustic phonon branches play a major role among all phonon branches to the total thermal conductivity of monolayer WS2, especially the longitudinal acoustic (LA) branch whose contribution percentage is 44.28%. There is a big band gap (no scattering) between the acoustic and optical branches, which is found to be responsible for the higher lattice thermal conductivity of monolayer WS2. This investigation could provide a reference and theoretical guidance for the design and improvement of monolayer WS2 based nano-electronic devices.