A three-dimensional mathematical model is proposed to study the behavior of molten pool and weld bead formation in variable-polarity plasma arc welding with wire feeding under flat and vertical-up welding conditions. An adaptive heat source that changes with the keyhole depth, tracked by the volume-of-fluid (VOF) method, is adopted in this study. As the energy and force of the plasma arc accumulating, a keyhole forms and increases in size, and the temperature and flow field of the molten pool change constantly. Through numerical results, the study found that the keyhole formation could be divided into three stages. Three forms of flow patterns in the molten pool were discovered in the keyhole formation process. The maximum fluid velocity of the molten pool is sharply increased initially, then moderately increased, and finally sharply decreased under the driving force of plasma flow. The established model is experimentally verified by the geometrical size of an experimental weld bead. This study may enhance the understanding of the dynamic interaction between the keyhole and molten pool, providing theoretical guidance to optimize the VPPAW process to obtain high-quality welds. (C) 2017 Elsevier Ltd. All rights reserved.