The keyhole plasma arc welding (K-PAW) is widely applied in engineering project now as a high energy beam welding with its advantages of low-cost and easy operation. However, the arc instability may arise and welding defects will be produced in K-PAW due to the high current and strong plasma penetrating force when medium thickness plates are welded, finally weakening the efficiency of K-PAW. Furthermore, it is found that the flow field of liquid metal in the molten pool and the stability of keyhole have a critical influence on welding quality. Therefore, modeling and simulating molten pool, keyhole and flow field in the K-PAW quasi steady process except for arc starting and ending phases are helpful to understand the welding process theory completely and promote its application further. But to date, there is little study on the coupled analysis of molten pool and keyhole in the quasi steady welding process due to the difficulty to make keyhole stable. In this work, based on the principles of fluid dynamics with considering arc pressure, surface tension, electromagnetic force, buoyancy and gravity, a three dimensional transient model is established to reveal the secondary changing of heat and force effect regularly as the keyhole depth increases. To describe the welding heat process, a combined type volumetric heat source model of 'double ellipsoid+conical body' is employed. A keyhole inside solid agitated (KISA) calculated method is proposed to maintain the keyhole stability in the quasi steady welding process. To improve the computational efficiency, the calculated region is limited within the action region of a cone-symmetrical weld heat source. With volume of fluid (VOF) method to track the keyhole boundary, the dynamic behavior process of molten pool, keyhole and flow field are calculated using FLUENT software. The stability of K-PAW is analyzed and the factors affecting keyhole production are discussed. The calculated results show that under the welding current 140 A and plasma gas flow 3.5 L/min, it needs 3.0 s to reach the quasi-steady state in which the average thickness of molten pool in keyhole front wall is 0.6 mm. The offset range of the keyhole center between top side and bottom side is 0.46~0.97 mm. There is the anticlockwise heat vortex appearing in molten pool of back side. The calculated width of keyholes on the bottom side is in good agreement with experimental results.