Facilitated olefin transport has been observed through membranes containing AgBF4 dissolved in poly(ethylene oxide) (PEO), but not through ones containing AgNO3 according to the previous studies. The difference in facilitated transport behavior between the two systems was theoretically investigated in terms of the mechanism on facilitated transport, in particular, the interaction of the silver cation with olefin using the density functional theory (DFT) method. It was found that the reaction of silver cation with ethylene occurred through two steps: (i) addition of one ethylene molecule to a silver cation dissolved in PEO, (ii) replacement of the ethylene molecule coordinated on the silver cation with another ethylene molecule. In the two-step mechanism of the addition and replacement reactions, the addition reaction is a nonactivated, preequilibrium process and the replacement reaction occurred through a transition state of two ethylene molecules coordinated to a silver cation dissolved in PEO. It was also found that the PEO/AgBF4 system was energetically more favorable for the facilitated olefin transport than the PEO/AgNO3 system. These results were well accordant with the experimental results.