In this study, we calculated the tooth root stress and the contact stress of involute- cycloid composite tooth profile spur gears with some design parameters such as the rolling circle radius, the pressure angle, and the tooth depth of the gears, which define the tooth profile. Then, we investigated the effects of the design parameters on the tooth root stress and the contact stress of the involute- cycloid composite spur gears from the calculation results. Furthermore, we calculated the tooth root stress and the contact stress with the error of center distance and examined the influence of the center distance on the tooth root stress and the contact stress of the involute- cycloid composite spur gears.