This work describes the development and the application of a quasi3D method for the simulation of turbochargers for automotive applications under unsteady flow conditions. The quasi3D approach is based on the solution of conservation equations for mass, momentum, and energy for unsteady flows and applied to zero-dimensional (0D) and one-dimensional (1D) elements arbitrarily oriented in the space. The compressor is divided into different regions, each one treated numerically in a different way. For the impeller region, a relative reference system has been used, and the presence of a centrifugal force field has been introduced both in the momentum and energy conservation equations. The direction of the ports at the inlet and outlet of the impeller are used to determine the design flow angles and therefore the deviation during off-design conditions. Conversely in the vaneless diffuser, the conservation of the angular momentum of the flow stream has been imposed in the tangential direction and then combined with the solution of the momentum equation in the radial direction. The model has been validated against measurements carried out on the test bench of the University of Genoa both in diabatic and adiabatic conditions.