On contemporary tokamaks, the control of the density is mainly performed with gas injection or with the injection of single type pellets (mm-sized body of frozen fuel). On future reactors, pellet injection is expected to be the main actuator available for core density control as gas injection is foreseen to be ineffective. It is anticipated that multiple pellet types (e.g., with varying size, injection velocity, composition) will be used. Hence, a control strategy that can control the density with multiple actuators is required. This work presents a model predictive controller (MPC) which can regulate the electron density profile of a tokamak fusion plasma using multiple pellet injectors and accounts for operational limits using constraints. This is the first MPC controller developed with the aim to control the density profile in a fusion reactor. Results of simulations with continuous and discrete pellet representations demonstrate the performance and robustness of the controller in the presence of plant-controller model mismatches.