A modeling of a turbo air compressor system (TACS), with a multi-level inverter for driving variable speed, combining an electrical model of an electric motor drive system (EMDS) and a mechanical model of a turbo air compressor, is essential to accurately analyze dynamics characteristics. Compared to the mechanical model, the electrical model has a short sampling time due to the high frequency switching operation of the numerous power semiconductors inside the multi-level inverter. This causes the problem of increased computational time for dynamic characteristics analysis of TACS. To solve this problem, the conventional model of the multi-level inverter has been proposed to simplify the switching operation of the power semiconductors, however it has low accuracy because it does not consider pulse width modulation (PWM) operation. Therefore, this paper proposes an improved modeling of the multi-level inverter for TACS to reduce computational time and improve the accuracy of electrical and mechanical responses. In order to verify the reduced computational time of the proposed model, the conventional model using the simplified model is compared and analyzed using an electronic circuit simulation software PSIM. Then, the improved accuracy of the proposed model is verified by comparison with the experimental results.