A GaAs/AlOx high contrast grating structure design which exhibits a 99.5% high reflectivity for a 425nm large bandwidth is reported. The high contrast grating (HCG) structure has been designed in order to enhance the properties of mid-infrared VCSEL devices by replacing the top Bragg mirror of the cavity. A robust optimization algorithm has been implemented to design the HCG structure not only as an efficient mirror but also as a robust structure against the imperfections of fabrication. The design method presented here can be easily adapted for other HCG applications at different wavelengths.