To reduce flow path loss caused by an intermediate plate or the like without reducing the strength of a cross-flow fan. Plural blades (40) extend in a lengthwise direction from a disc-shaped or circular annular support plate. A ring portion (61) of an auxiliary ring (60) is positioned on a lengthwise direction intermediate section of the plural blades (40) and is disposed on the outside of outer ends (40a) of the plural blades (40). Plural connection portions (62) of the auxiliary ring (60) extend from the ring portion (61) as far as spaces between adjacent blades of the plural blades (40) and are joined to the blades (40) in the spaces between adjacent blades.