The primary challenge during the secondary bonding process of full-height honeycomb sandwich structures is the aramid honeycomb core’s height shrinkage. This paper systematically investigated the height evolution behavior of the honeycomb core by using a creep testing machine. The results showed that the out-of-plane compression deformation curve of aramid honeycomb cores is mainly divided into three stages: the dehumidification stage, the pressurization stage and the creep stage. Under conditions of high temperature and pressure, height shrinkage was attributed to the dehydration caused by moisture infiltration, and the compression creep resulted from the slippage of polymer molecular chains. Dehydration shrinkage is stable, whereas compression creep reflects typical viscoelastic polymer characteristics. By employing the viscoelastic Burgers mechanical model and applying the nonlinear surface fitting method, the total height shrinkage deformation behavior of the aramid honeycomb core during the curing process can be accurately predicted by summing the above three stages. This research contributes valuable insights for the manufacturing process of honeycomb sandwich structures.