The reasonable selection of three-dimensional roughness parameters can evaluate the service performance of the machined surface, and its excessively high dimension greatly increases the difficulty of selection. In order to reveal the correlation law between the 3D roughness parameters and the tooth surface contact performance parameters, the correlation analysis theory is used to explore the correlation, and the nonlinear mapping model is constructed by using the BP neural network, the genetic algorithm optimization and Morris and Sobol′ two global sensitivity. The qualitative analysis method conducts the qualitative and quantitative analysis of each parameter, selects the three-dimensional roughness parameters that have the greatest impact on the contact performance of the tooth surface, and determines the primary and secondary relationship, solves the problem of parameter redundancy, and provides the theoretical basis for the anti-fatigue design and manufacturing of the tooth surface. The results show that the overall influence of the maximum shear stress on the gear tooth contact and the maximum surface pressure are arranged in the following order: the arithmetic average height (Sa) and the peak volume (Vmp), in which Sa has a strong correlation.