We study the first-order Verwey transition in single-crystal Fe3O4 using high-resolution temperature-dependent (100-300 K) photoemission spectroscopy. The near-Fermi-level (EF) spectrum exhibits a clear gap of ∼70 meV in the occupied part of the density of states (DOS) in the low-temperature semiconducting phase. The gap is closed above the transition temperature TV=122 K, establishing a metal-semiconductor transition. The Fe 3d derived features arising from Fe3+ (eg2) majority- and Fe2+ (t2g1) minority-spin states responsible for the transition retain their character just above the transition but merge into a single feature by 300 K. Simultaneously, the DOS at EF increases systematically in the metallic phase. The results indicate the existence of, and a gradual change in, the short-range order for T>TV, which causes the nonmetalliclike electrical conductivity observed just above TV.