This paper considers the problem of controlling bead geometry of a Gas-Metal Arc Weld (GMAW). Specifically, the desire is control bead width and depth in real-time, and travel speed of the torch and wire feedrate are chosen as the inputs. Previous work has shown that process dynamics are highly non-linear, and this is quantified for this problem through a series of experiments and off-line parameter identification experiments. Since the range of parameter variations can be as large as ± 40%, adaptive control is investigated to achieve high performance. A multi-variable deadbeat adaptive control algorithm is investigated and implemented to achieve the desired weld bead geometries. Control weighting factors are introduced to reduce the excessive control effort that is likely to exist in the deadbeat algorithm. Simulation results indicate that the weighted deadbeat adaptive controller works well for the welding process, and that the control weighting factors are essential to practical, non-saturating control performance.