While a relatively complete understanding of the nucleation and orientation of polymers under confinement in one-dimensional nanochannels has been achieved, crystallization kinetics investigation of confined polymers is still rare. In this work, we investigated the crystallization kinetics of poly(ethylene oxide) confined in anodic alumina oxide templates with different pore sizes using in situ wide-angle X-ray scattering (WAXS). The crystallization kinetics results were fitted with the Avrami equation. The Avrami index was determined by both "isothermal step crystallization" and in situ WAXS. The crystallization process of polymers under one-dimensional nanopore confinement was simulated by a "one-dimensional lattice model". Based on this model, it is shown that homogeneous nucleation with the simultaneous growth of multiple crystal planes with drastically different growth rates could result in Avrami indexes lower than 1.