This paper reports that ~10-nm-thick iron selenide (FeSe) thin films exhibit insulator-like behavior in terms of the temperature dependence of their electrical resistivity even though bulk FeSe has a metallic electronic structure that has been confirmed by photoemission spectroscopy and first-principles calculations. This apparent contradiction is explained by potential barriers formed in the conduction band. Very thin FeSe epitaxial films with various atomic composition ratios ([Fe]/[Se]) were fabricated by molecular beam epitaxy and classified into two groups with respect to lattice strain and electrical properties. Lattice parameter a increased and lattice parameter c decreased with increasing [Fe]/[Se] up to 1.1 and then a levelled off and c began to decrease at higher [Fe]/[Se]. Consequently, the FeSe films had the most strained lattice when [Fe]/[Se] was 1.1, but these films had the best quality with respect to crystallinity and surface flatness. All the FeSe films with [Fe]/[Se] of 0.8-1.9 exhibited insulator-like behavior, but the temperature dependences of their electrical resistivities exhibited different activation energies E a between the Se-rich and Fe-rich regions; i.e., E a were small (a few meV) up to [Fe]/[Se]=1.1 2 but jumped up to ~25 meV at higher [Fe]/[Se]. The film with [Fe]/[Se]=1.1 had the smallest E a of 1.1 meV and exhibited an insulator-superconducting transition at 35 K with zero resistance under gate bias.The large E a of the Fe-rich films was attributed to the unusual lattice strain with tensile in-plane and relaxed out-of-plane strains. The large E a of films with [Fe]/[Se]>1.1 resulted in low mobility with a high potential barrier of ~50 meV in the conduction band for percolation carrier conduction compared with that of the [Fe]/[Se]=1.1 film (~17 meV). Therefore, the Fe-rich films exhibited remarkable insulator-like behavior similar to a semiconductor despite their metallic electronic structure. The high potential barrier of Fe-rich films is tentatively attributed to the presence of large amounts of excess Fe, which could plausibly cause a broad superconducting transition without zero resistance under gating.