The PEO3:LiCF3SO3 polymer electrolyte has attracted significant research due to high conductivity and enhanced stability in lithium polymer batteries. Most experimental studies have shown that amorphous PEO lithium salt electrolytes have higher conductivity than the crystalline ones. Other studies, however, have shown that crystalline PEO salt complexes can conduct ions. As a result, further theoretical investigations are warranted to help clarify the issue. In this work, we use density functional theory with the climbing image nudged elastic band method to investigate the atomic-scale mechanism of lithium ion transport in the polymer electrolytes. We also use density functional theory and ab initio molecular dynamics simulations to obtain the amorphous structure of PEO3:LiCF3SO3. The diffusion pathways and activation energies of lithium ions in both crystalline and amorphous PEO3:LiCF3SO3 are determined. In crystalline PEO3:LiCF3SO3, the activation energy for the low-barrier diffusion pathway is approximately 1.0eV. In the amorphous phase, the value is 0.6eV. This result would support the experimental observation that amorphous PEO3:LiCF3SO3 has higher ionic conductivity than the crystalline phase.