This paper deals with the optimum design of the involute-cycloid composite tooth profile helical gear, which was developed as a non-involute tooth profile gear based on cycloid tooth profile. The involute-cycloid composite tooth profile helical gear has some design parameters such as pressure angle and rolling circle, which define the involute-cycloid composite tooth profile curve. In this study, we developed a method to calculate the tooth root stress and the tooth contact stress of the involute-cycloid composite tooth profile helical gear. Then we compared the results with the experimentally measured data, and the validity of the present calculation method was certified by the good agreement of the calculated values with the measured data. Furthermore, we discussed the effects of the design parameters on the tooth bending and tooth contact strengths of the involute-cycloid composite tooth profile helical gear.