This paper presents a design optimization process for interior permanent magnet synchronous motors (IPMSM) for hybrid electric compressors (HEC) which are applied to hybrid electrical vehicles. A hybrid electric compressor is composed of an electric motor driving section and an engine driving section which is connected to the engine by a pulley belt. A hybrid electric compressor driving motor requires half of the full driving power of a compressor. Even though an engine is not operated at the idling stop mode, the electric motor drives the air-conditioner compressor by itself so that the air conditioning system can produce its minimum cooling capacity. In this paper, the design optimization of an IPMSM for a 42 (V) applied voltage system is studied using the design of experiment (DOE) and response surface method (RSM) of 6sigma. The driving characteristics of this motor drive system are measured and analyzed by experiment.