The constitutional model is crucial to model the complex response of woven carbon fiber reinforced plastics (CFRPs) during curing. This study developed a multiscale modeling method to describe the viscoelastic behavior of preformed woven CFRP parts during curing. The essence of the viscoelastic modeling lies in the stiffness matrix, which was predicted via the long-short term memory (LSTM) model. A library of viscoelastic stiffness components for the LSTM model was created through finite element method (FEM) on mesoscopic representation volume elements (RVEs). Specifically, FEM models for RVEs with different configurations were established first, and then utilized for virtual relaxation tests to build the stiffness component library for the woven CFRP. Afterwards, the LSTM model was embedded into the material model for FEM at the part-level. Finally, prediction accuracy of the multiscale modeling method for viscoelasticity of the woven CFRP samples were validated by experiments with the average error of 6.62%.