Understanding capillary filling dynamics in nanoconfined geometries is crucial in the nanotechnology field, such as nanofluidic devices, lab-on-a-chip, 3D printers, porous nanomaterials. The spontaneous capillarity-driven flow behaviors of polyethylene (PE) melts through anodized aluminum oxide (AAO) nanopores are investigated experimentally by using the nanoporous template wetting technique first in our study. The diameter of the pores is 100 nm and 200 nm. The displacement of the polymer melts is measured by the thickness of the fabricated nanowire array as a function of time. Besides, considering the effect of the shear rate on the polymer viscosity in the capillary nanoflow, a theoretical model, i.e. a modified Lucas–Washburn law that combines the Lucas–Washburn law with the polymer rheological model, is established. Based on the experimental results it is speculated that the rise of the meniscus agrees with the modified Lucas–Washburn law. It also suggests that the zero-shear-rate viscosity of the PE melts decreases in their flows through the nanopores and the induced unconventional rheological behavior may be caused by nanoconfinement of the nanopores.