In view of the problems of the complex design, difficult machining, and high manufacturing cost of a traditional nutation reducer, this paper intends to design a nutation reducer and study its meshing performance. First, the meshing pair is designed by the method of internal and external cutting of the shaper cutter, and the method of face gear tooth surface modification is proposed. Second, based on tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA), the contact performance of the meshing pair is studied. Then, the nutation reducer is improved by using the pair instead of the internal bevel gear pair. Finally, examples are presented to test the feasibility of the improved design. The results show that the improved nutation reducer maintains the advantages of a large transmission ratio and high bearing capacity of the traditional nutation reducer and can make use of the advantages of face gears to further improve its transmission performance. This study can lay a foundation for the further application and popularization of nutation reducers.