Methods for controlling tension and velocity in Roll-to-Roll (R2R) processes have been widely studied in literature. Such methods are very effective under normal operating conditions, but the performance will degrade when control efforts saturate the physical capability of systems. This paper presents a constrained linear-quadratic model predictive control (LQ-MPC) scheme for the purpose of reference tracking. Firstly, a discrete-time linearized model for a R2R process is derived based on the governing equations from prior studies. The model is augmented by integrating an incremental behavior into it. Then a model predictive controller is specifically designed to reach zero-offset tracking of tension and velocity references, while the encountered process constraints are enforced at the same time. The constrained control problem is reduced into a quadratic programming problem and solved by using gradient projection method. It is proved that the proposed controller can guarantee local closed-loop stability where process constraints are inactive. Simulation of a five-roller R2R system is conducted to compare the performance of a proposed controller and a typical decentralized PI controller. Results show that the proposed controller achieves better performance in terms of quick response to changing of set points and capability of decoupling the subsystems. It also demonstrates good robustness when reasonable parametric uncertainties are introduced in the system.