The tooth bending and tooth contact strengths of the involute-cycloid composite tooth profile helical gear, which was developed as a non-involute tooth profile gear based on cycloid tooth profile, are directly affected by its tooth profile. The involute-cycloid composite tooth profile curve changes with some design parameters such as pressure angle and radius of rolling circle. 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 tooth root and tooth contact stresses calculated by this method 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 considering the results of the tooth root and the tooth contact stresses calculated in the case of various values of the design parameters.