The present research article aims to obtain good weld integrity and avoid material fracture due to high welding temperature. The Computational Fluid Dynamics (CFD) and Finite Element Method (FEM) were used to study GTAW process. The heat source distribution and the convection movement in the melted pool were taking into account. In fact, a two-dimensional (2D) numerical model has been developed for GTAW process and applied for 304L stainless steel. The effects of welding operating parameters were discussed such as voltage and current. The simulation showed that capillary force presented by Marangoni convection affects mainly the weld pool geometry. Therefore, as a result, increasing the welding power and specially the current intensity leads to the growth of the melted zone rapidly, which may induce high residual stress and risks of metal failure. Finally, comparing computed weld profile with the experimental results showed good agreement.