A cooling and heating system of a battery for a vehicle is provided. The system includes a battery module that provides driving energy to the vehicle and an electric component that drives the vehicle using the driving energy of the battery module. An air passage unit of the system includes a radiator disposed therein, a first flow path through which the air passing through the electric component of the vehicle is introduced, a second flow path through which the air passing through the radiator is discharged to the outside of the vehicle, and a door that for selectively opens and closes the first flow path and the second flow path. A controller operates the door to open or close.