Downsizing engines with a turbocharging system have been widely applied to passenger cars to improve fuel economy. Engine torque response to accelerator operation is one of important features in addition to steady state performance of the system. Torque profile management for turbocharged internal combustion engines is one of required technologies.A turbocharging system for a car is a system with a positive feedback loop in which compressed air drives the compressor after the combustion process. A reduced order model was derived for the charging system. Pressure ratio of a compressor is proportional to square of turbine speed and the turbine speed is a first order delay system to throttle opening in the model.Model structure was designed from mathematical equations that describe turbine and compressor works. Model parameters were identified from measured data. An output torque profile control strategy based on the derived model is investigated.