There are few studies on the influence of tooth profile parameters on the stress of composite cycloid planetary gear pair. In this study, by using the fourth-order composite cycloid as the internal tooth profile, the conjugate tooth profile was designed based on Lewis theorem, and the cycloid tooth profile was modified. Finally, the solid model was established for finite element analysis, and the effects of tooth profile parameters on the stress of compound cycloid gear were analyzed. The results show that the compound cycloidal planetary gear transmission is a multi-tooth meshing transmission. The stress distribution is the typical Hertz contact at the meshing contact position, and there is a slight stress concentration area at the tooth root. The bearing capacity of gear pair is mainly limited by the contact fatigue strength of tooth surface. If possible, a larger modulus, a larger tooth height adjustment coefficient and a smaller tooth shape adjustment coefficient should be selected to improve the bearing capacity of the gear pair.