During the last two decades, Model Predictive Control (MPC) has established itself as an important form of advanced control due to its ability to deal with constraints. This results in demanding on-line optimization, hence computing resource can become an issue when applying MPC to complex systems with many inputs or with fast response times. In this thesis, a novel algorithm, called the Multiplexed MPC is proposed. The Multiplexed MPC scheme divides the MPC problem into a sequence of smaller optimizations, solves each subsystem sequentially and updates subsystem controls as soon as the solution is available, thus distributing the control moves over a complete update cycle while the total number of control moves in a given period remains the same as that of the original MPC problem. This results in reduced computational complexity and thus shorter computational time. This reduction in computational complexity allows Multiplexed MPC to be executed at higher sampling rate, which in turn reacts faster to disturbances and thus can lead to improved performance in some cases, despite finding sub-optimal solutions to the original problem. Stability of the Multiplexed MPC is established in this thesis.