An important paradigm for the modelling of naturally aspirated (NA) spark ignition (SI) engines for control purposes is the Mean Value Engine Model (MVEM). Such models have a time resolution which is just sufficient to capture the main details of the dynamic performance of NA SI engines but not the cycle-by-cycle behavior. In principle such models are also physically based, are very compact in a mathematical sense but nevertheless can have reasonable prediction accuracy. Presently no MVEMs have been constructed for intercooled turbocharged SI engines because their complexity confounds the simple physical understanding and description of such engines. This paper presents a newly constructed MVEM for a turbocharged SI engine which contains the details of the compressor and turbine characteristics in a compact way. The model has been tested against the responses of an experimental engine and has reasonable accuracy for realistic operating scenarios.