A cross-flow fan includes a disc-shaped or circular annular support plate, plural blades extending in a lengthwise direction from the support plate, and an auxiliary ring. The auxiliary ring has a ring portion that is positioned on a lengthwise direction intermediate section of the plural blades and is disposed on an outside of outer ends of the plural blades, and plural connection portions that extend from the ring portion as far as spaces between adjacent blades of the plural blades and are joined to the blades in the spaces between adjacent blades.