Disclosed in the present invention is an apparatus for eliminating stress spots on a surface of glass, comprising a conveying assembly, provided with a conveying surface for reciprocally conveying the glass along a conveying direction; an upper air-blowing assembly, provided above the conveying surface, used for guiding air to reciprocally flow above the conveying surface along a swinging direction extending along a width direction of the glass; and a lower air-blowing assembly, provided under the conveying surface, used for guiding air to reciprocally flow under the conveying surface along the swinging direction. A method for eliminating stress spots on a surface of glass comprises a conveying step, a glass swinging step, and an air-cooling step.