A skilled welder determines the weld joint penetration from his/her observation on the weld pool surface during the welding process. This paper addresses the estimation of weld joint penetration (i.e. determining back-side bead width that measures the degree of the weld joint penetration in full penetration welding) using the parameterized 3D weld pool surface in gas tungsten arc welding (GTAW). To this end, an innovative machine vision system is used to measure the specular weld pool surface in real-time. Various experiments under different welding conditions have been performed to produce full penetration welds with different back-side bead widths and acquire corresponding images for reconstructing the weld pool surface and calculating candidate estimation parameters. Through the least squares algorithm based statistic analyses, it was found that the width, length, and convexity of the 3D weld pool surface provides the optimal model to predict the back-side bead width with an acceptable accuracy. A foundation is thus established to effectively extract information from the weld pool surface to facilitate a feedback control of the weld joint penetration.