The polymerization process, as the starting point of polyester fibre production, directly affects the fibre properties. However, the polymerization process has complex reaction mechanisms and involves many variables, making online modelling more challenging. In this paper, we introduce the Copula function into the modelling of the polymerization process. First, a feature selection method based on kernel principal component analysis (KPCA)-Copula is proposed, and then, the Copula function to obtain the nonlinear characteristics among the variables is used. On this basis, an online prediction model of intrinsic viscosity based on just-in-time learning (JITL) was established, that is, empirical Copula-JITL. In order to improve the computational efficiency of the empirical Copula-JITL, the t-Copula function is introduced. Furthermore, by combining the t-Copula function with the empirical Copula function, we get a JITL model based on the hybrid Copula function, that is, hybrid Copula-JITL. Finally, actual polymerization process data collected from fibre production are provided to demonstrate the effectiveness of the proposed algorithms.