Air-handling units (AHUs) have become indispensable parts of heating, ventilation, and air conditioning (HVAC) systems. AHUs are also significant energy consumers due to the function of their several actuators. Many recent works focus on improving the control techniques of AHUs to provide better indoor comfort with lower energy consumption. However, due to its inherent structure, it is complex to design an optimal and adaptive control for AHU that fulfills this mission in all operation conditions. Model predictive control (MPC), in this context, has been in focus in many contributions recently. However, designing a multi-input multi-output (MIMO) MPC for AHU optimal control is not a trivial task due to the difficulty of having a high-fidelity mathematical model. This study proposes and validates a data-driven nonlinear MPC with MIMO architecture. The proposed MPC is based on the sparse nonlinear dynamic of AHU built upon operation data of a real AHU installed in the KTH live-in lab. In contrast to the classical approaches, the proposed MPC adjusts simultaneously five different actuators to control the supply temperature. This article presents a simulation study for the performance of the proposed MPC framework under different control configurations.