The three-dimensional transient computational fluid dynamics model of heat and mass transfer in the wire arc additive manufacturing (WAAM) process of TA31 titanium alloy was established. Through the volume of fluid method, the free surface was tracked. The dynamic evolution of droplet growth, liquid bridge transfer, and detachment from the wire tip into the molten pool was calculated. The velocity field of the molten pool driven by surface tension, arc pressure, arc shear, electromagnetic force, gravity, and buoyancy was calculated. The validity of the numerical model was confirmed through the results of high-speed imaging and the cross-sections of weld bead. Results show that the liquid bridge transfer mode exerts less effect on the molten pool, which is conducive to reduce the irregularity of the bead surface. With expanding the molten pool, the height of weld bead is firstly increased, then decreased, and finally becomes stable. Under the influence of arc pressure and surface tension, a crater forms on the molten pool surface, and the convection occurs inside the molten pool. The inertial force and surface tension are the most important dynamic forces in the liquid bridge transfer process, and the influence of viscosity and gravity can be neglected.