With the goal of minimizing fuel consumption and torque tracking error, while also avoiding knock and misfire, a traditional engine controller may be conservative since it does not consider transient behavior. In this paper, an approximate nonlinear model predictive control (NMPC) is presented for use on a gasoline engine with exhaust gas recirculation (EGR). In the NMPC framework, a nonlinear dynamic model of the engine is used to train a state feedback controller, while also considering the constraints. The resulting controller is implemented as look-up tables that are fast to compute in real time. An unscented Kalman filter is used for state estimation. Testing on a benchmark engine simulator shows a significant performance improvement over the baseline controller.