Since the welding process is complex and highly nonlinear, it is very difficult to accurately model the process for real-time control. In this paper, a discrete-time transfer function matrix model for gas metal arc welding process is proposed. Although this linearized model is valid only around the operating point of interest, the adaptation mechanism employed in the control system render this model useful over a wide operating range. A multivariable one-step-ahead adaptive control strategy combined with a recursive least-squares method for on-line parameter estimation is implemented in order to achieve the desired wield bead geometries. Command following and disturbance rejection properties of the adaptive control system for both SISO and MIMO cases are investigated by simulation and experiment.