This paper presents the optimization process of evaporator for a vapor compression cooling system for high heat flux CPU. The CPU thermal capacity was given by 300W. Evaporating temperature and mass flow rate were $18^{circ}C$ and 0.00182kg/s respectively. R134a was used as a working fluid. Channel width(CW) and height(CH) were selected as design factors. And thermal resistance, surface temperature of CPU, degree of superheat, and pressure drop were taken as objective responses. Fractional factorial DOE was used in screening phase and RSM(Response Surface Method) was used in optimization phase. As a result, CW of 2.5mm, CH of 2.5mm, and CL of 484mm were taken as an optimum geometry. Surface temperature of CPU and thermal resistance were $33^{circ}C;and;0.0502^{circ}C/W$ respectively. Thermal resistance of evaporator designed in this study was significantly lower than that of other cooling systems such as water cooling system and thermosyphon system. It was found that the evaporator considered in this work can be a excellent candidate for a high heat flux CPU cooling system.