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This paper describes a model predictive control (MPC) strategy to optimize the operation of a building HVAC system with phase change material-based energy storage integrated in supply air ducts. The control problem is nonlinear due to the piece-wise linearity of the PCM dynamics and dependence of the convective heat transfer coefficient on variable airflow. To eliminate the nonlinearity, a set of discrete airflow rates are used and the airflow mode switches are optimally scheduled through a MPC implementation. A mixed-integer linear program (MILP) is formulated for the MPC problem by using the classic big M method and is solved with mature MILP solvers. The developed MPC method was tested and compared to a baseline control strategy via simulation tests. The results showed that the developed strategy could lower the demand and energy charges by 30% and 8.1%, respectively.