Tetragonal PbSnF4 synthesized by a solid-state reaction at 523-573 K under an HF gas atmosphere showed a transition to a monoclinic phase between 20 and 77 K. Its structural changes were studied at 20-300 K using the Rietveld analysis of TOF neutron diffraction data. The structure of PbSnF4 is basically composed of the fluorite lattice and the cationic framework made up of layers perpendicular to the c-axis with a sequence of Pb-Pb-Sn-Sn. At 20 K, the monoclinic structure has no fluoride ions on the F(1) tetrahedral site which is situated between two Sn layers. The interstitial F(4) site situated between Sn and Pb layers splits into two sites near a large cavity in an F8 cube. These sites split into four at 170 and 300 K; the change in the interstitial structure corresponds to the monoclinic-to-tetragonal phase transition. Above 170 K, fluoride ions at the F(2) tetrahedral site migrate gradually to the F(1) site. A gradual slope change in the conductivity versus temperature curve around room temperature corresponds to the migration of fluoride ions.