The new type of nutation reducer with double circular-arc bevel gears as the core is characterized by advantages such as high load-bearing capacity, large transmission ratio, and simple structure. The existing research focuses on the machining methods of gears and the analysis of tooth contact. This article first time establishes an elastohydrodynamic mixed lubrication model for nutation double circular-arc bevel gear. The model's accuracy is verified by comparing it with existing test results. On this basis, combined with the finite element method and tooth contact analysis, the meshing characteristics, tooth contact characteristics, and lubrication characteristics of the double circular-arc bevel gear tooth surface are analyzed. The results show that the entrainment velocity at the contact point of the tooth surface during transmission is much higher than the sliding velocity. Consequently, the meshing motion is close to pure rolling. In constant-speed transmission, the oil film thickness at the engaging-in and exit points near the edge of the tooth surface is smaller than that at other meshing points on the tooth surface. This phenomenon can easily lead to mixed lubrication and lubrication failure, as well as tooth surface wear. During deceleration, i.e., when the speed drops to 50 r/min, the oil film thickness approaches zero, indicating that the gear has entered a mixed lubrication state. The proposed model can be used for lubrication analysis and improving transmission accuracy of nutation double circular-arc bevel gears.