Machine learning demonstrates significant superiority in the prediction of rheological properties of polyacrylonitrile (PAN)-based carbon fiber spinning solution. However, collecting large-scale datasets for training and calibrating hyperparameters remains a considerable challenge due to the high complexity of polymer-related experiments and simulations. This study employs the Physics-Informed Gaussian Process Regression (PIGPR) method to construct a predictive model driven by limited data, based on the interactions between polymers and their properties. It integrates prior knowledge from both macroscopic and microscopic rheological physics models of polymers, formulating the regression problem within a multi-task learning framework. This framework combines experimental measurement data with targets derived from physical models to optimize the kernel function’s hyperparameters, using prior knowledge to define the mean function. Experimental results indicate that the PIGPR effectively facilitates Bayesian inference with fewer data points, providing an efficient approach for domains where measurements are expensive and time-consuming. Additionally, the model delivered predictions for the rheological properties of carbon fiber spinning solutions that closely matched both experimental and simulated data, validating its effectiveness. The integration of physical information demonstrates strong fitting, interpretability, and extrapolation capabilities, offering robust guidance for subsequent experimental design and simulation efforts.