Structures of small sodium fluoride cluster cations, NanFn-1+, have been determined for n = 5-23 by ion mobility mass spectrometry. In the mass spectrum of NanFn-1+ cluster ions measured after collisions in the ion-drift cell, cuboid ions with near-regular hexahedron such as n = 14 (3X 3 X 3), 23 (3 X3 X 5), 38 (3 X 5 X 5), 63 (5X 5X 5), and 88 (5 X 5 X7) were predominantly observed as magic numbers. By comparison of the collision cross sections obtained from the ion mobility measurements with theoretical ones, we have experimentally shown that the ions of n = 7 and 10 have stable non-rock-salt type structures in which one sodium atom is encapsulated into the sodium fluoride cuboid lattice. The collision cross sections of n = 12 and 13 are almost equal to that of the n = 14 cuboid. A similar feature was also observed in collision cross sections of n = 21 and 22, which are equal to that of the n = 23 cuboid. These features indicate that the cluster ions of n = 12, 13, 21, and 22 have near-cuboid structures with some surface defects.