This paper deals with air-fuel ratio control for a gasoline combustion engine. The proposed approach is based on tracking of fuel mass flow reference using a nonlinear model of air and fuel path dynamics in cylinder. To maintain the model accuracy while keeping its complexity on an acceptable level, we propose to employ an optimal piecewise affine approximation of the derived nonlinear model, covering the entire operating range of the real system. The resulting hybrid model is subsequently used for model predictive control synthesis, where the formulated optimization problem is solved online by mixed-integer quadratic programming. To evaluate the tradeoff between complexity and performance of the obtained controller, it is compared with the one obtained by nonlinear programming exploiting the full nonlinear model. The simulation results show that even a relatively low-complex approximation leads to a satisfactory air-fuel ratio control performance while allowing for potential practical implementation on a real engine.