The ion-transport phenomenon, determined by the interaction of strain and electrostatic energy, is one of the most important examples that confirms the effects of the polymorphism and atomic morphology. We investigated the correlation between the structural morphology and Li-ion conduction characteristics in α-Li3PS4, a high-temperature phase of the Li3PS4, using ab initio molecular dynamics (AIMD) calculations. We successfully reproduced the thermal disorder and partial occupancy observed at high temperatures by AIMD and confirmed the Li-ion sites and its migration pathways. The activation energy and Li-ion conductivity of α-Li3PS4 at room temperature were predicted to be about 0.18 eV and 80 mS cm-1, respectively, indicating that α-Li3PS4 is one of the fastest Li-ion conductors known so far. The fast Li-ion conduction in α-Li3PS4 is mainly caused by the BCC S-sublattice and tetrahedron-tetrahedron pathway with fully occupied Li-ion sites. Therefore, α-Li3PS4 having a BCC S-sublattice offers a promising structural morphology for effective Li-ion conduction.