Waxy crude oil exhibits shear-dependent and time-dependent thixotropic behavior below the threshold temperature. Various models have been proposed to describe this type of behavior in previous literature reports. Due to the complexity of thixotropic behavior, the models with good-description ability generally contain a large number of parameters, which results in the difficulty of parametric regression. The double-structural-parameter model shows common features of complex thixotropic models, i.e., containing a great many parameters and possessing a good fitting effect, and it is a representative model for the study of parametric regression. In this study, the double-structural-parameter model is introduced, and three regression strategies of this model are proposed. To obtain an excellent fitting effect as much as possible and make an estimation of the obtained parameters easy, an advanced self-adaptive differential evolution algorithm is adopted, and then it is improved to accommodate parametric regression. Through the implementation of parametric regression, it is found that the obtained partial parameters show unstable characteristics for three regression strategies of the double-structural-parameter model. By in-depth analysis of the results, the unstable phenomenon is explained, and it can be avoided by using a new thixotropic experimental method. The final regressive results indicate that the regression strategy III can compromise a good fitting effect and physical interpretation, and it is recommended in this study. In addition, it is pointed out that the fitting effect, stability of parameters, and physical interpretation should be considered simultaneously for the parametric regression. Although this study is conducted on the basis of the double-structural-parameter model, it can provide beneficial guidance to parametric regression of other complex thixotropic models or even other multiparameter models in other research fields.