The paper deals with trajectory tracking of the differential drive robot with a mathematical model governing dynamics and kinematics. Motor dynamics and chassis dynamics are considered for deriving a linear state-space dynamic model. Basic nonlinear kinematic equations are linearized into a successively linearized state-space model. The dynamic and kinematic models are augmented to derive a single state-space linear model. The deviation variables are reference variables which are variables of an ideal robot following a reference trajectory which can be pre-calculated. Reference tracking is achieved by model predictive control of supply voltage of both the drive motors by considering constraints on controlled variables and manipulated variables. Simulation results are provided to demonstrate the performance of proposed control strategy in the MATLAB simulation environment.