A single-crystalline film of Sr2CoO4 with square-lattice CoO2 sheets (K2NiF4-type structure) was synthesized, and its electronic properties were characterized. The compound exhibited both ferromagnetic and metallic behaviors, with a fairly high Curie temperature T(C) of approximately 250 K, in contrast to the superconductivity recently found in a triangular-lattice CoO2-sheet compound. The film's large magnetoresistance with current perpendicular to the CoO2 plane showed field-hysteretic behavior analogous to tunneling magnetoresistance. The electronic structure of Sr2CoO4 was also investigated to characterize the quasi-two-dimensional ferromagnetic metal state in terms of optical spectroscopy and first-principles calculation.