The variable hyperbolic circular arc tooth trace (VH-CATT) cylindrical gear is a new gear suitable for heavy loads and high speed. The special structure of the gear provides excellent mechanical properties but also increases the processing difficulty. The special machine tool for VH-CATT gear provides a prerequisite for mass production, but the machining accuracy remains to be improved. Therefore, this paper proposes a Kriging model based on the glowworm swarm optimization algorithm of scene understanding (SGSO) to study the relationship between input parameters and output precision. Then, the SGSO algorithm is used to optimize the parameters of the Gaussian mutation function in the Kriging model to improve its fitting accuracy. When solving four groups of tooth profile and tooth direction errors, the key precision index, R², of SGSO-Kriging all exceed 0.95. Additionally, the feasibility of the model is verified by the residual diagram and the box diagram. The contour diagram and error results show that reducing the feeding velocity, v_f, can improve accuracy most efficiently, and the increase of rotational speed, n, is more conducive to the accuracy of the tooth surface than the acceleration of the coolant, v_Q. The above research provides an optimization strategy of gear machining accuracy and a theoretical basis for the promotion of the VH-CATT gear.