In this paper, a model-based strategy for the air-path, fuel injection timing, and fuel pressure control of a heavy-duty Diesel engine is presented. The engine system is a six-cylinder Diesel engine, equipped with a dual-stage fixed geometry turbo system and a variable valve actuation (VVA) system. The VVA operates on the intake valves, and realizes a late Miller combustion cycle. The control strategy implemented is a multilinear-model predictive control (MPC), which manipulates the intake valve hold and closure timing, the fuel injection timing, and the needle opening pressure. The MPC objectives are: (i) to keep NOx emissions under a reference level, (ii) to keep the air-fuel ratio over a certain reference, while (iii) minimizing fuel consumption under other constraints. The use of a model predictive control strategy is motivated by the fact that the system is a multi-input multi-output system, with several constraints applied to it. This paper presents the applied control strategy and simulation results illustrating the potential of the proposed control. The simulation results show that the control strategy is applicable, and that the fuel consumption is minimized, but also that further refinements are required.