The first-principles electronic structure calculation is carried out to predict that a chromium oxide K2Cr8O16 with the hollandite-type crystal structure should be a new half-metallic ferromagnet. We compare our results with recent experimental data which indicate the ferromagnetic-metal to ferromagnetic-insulator transition at T ∼ 90 K, as well as the paramagnetic-metal to ferromagnetic-metal transition at T ∼ 180 K. Based on the calculated electronic structures, we argue that the double-exchange mechanism is responsible for the observed saturated ferromagnetism and the formation of the incommensurate, long-wavelength density wave of spinless fermions caused by the Fermi-surface nesting may be the origin of the opening of the charge gap.