In this paper, a lane-keeping system is proposed for the tractor with two articulated trailers. For Tractor with Multi-Unit Trailer (T-MUT) vehicles, the motions of each unit of the vehicle are quite different from those of ordinary single-unit vehicles. Based on the dynamic model of the T-MUT vehicle, the lane-keeping control system of a T-MUT vehicle is designed with Model Predictive Control (MPC). In order to consider the uncertainty of the weight change at each trailer, a model uncertainty analysis is performed through the transfer functions for each hitch angle. For lane-keeping performance, the geometry constraints on each unit of the T-MUT vehicle are described to prevent the vehicle from lane invasion. Also, by applying the constraint tightening method to the output of the controller, a robust MPC is designed against model uncertainty, such as weight changes at each trailer. The performance of the proposed controller is validated in simulations with various curvature scenarios.