Provided is a composition for a non-aqueous secondary battery functional layer capable of forming a functional layer that can provide a battery member such as an electrode or a separator with both excellent blocking resistance and excellent process adhesiveness. The composition for a functional layer contains a particulate polymer A. The particulate polymer A has a core-shell structure including a core portion and a shell portion that at least partially covers an outer surface of the core portion. The core portion is formed from a polymer having a glass-transition temperature of higher than 25° C. and lower than 80° C. The shell portion is formed from a polymer having a glass-transition temperature of −80° C. to 25° C. The proportion constituted by the core portion among the total of the core portion and the shell portion is 30 mass % to 80 mass %.