The invention discloses the technical field of railway track engineering construction and particularly relates to a mounting device for a foam board for a track bed expansion joint and an operation method thereof. The mounting device for the foam board for the track bed expansion joint comprises two clamping pieces arranged below a steel rail side by side. Each clamping piece comprises a clamping face. A clamping space for clamping the foam board is formed between the two clamping faces. Tensioning devices used for making the distance between the clamping pieces close are arranged on the two clamping pieces. When the clamping pieces are used for clamping the foam board, the clamping faces of the clamping pieces are perpendicular to the horizontal plane. The two clamping pieces including the clamping faces are arranged side by side, and the clamping space is formed between the clamping faces of the two clamping pieces, so that when the foam board is mounted, by clamping the foam board, it is guaranteed that the problems of offset, deflection and the like of the foam board do not occur; and by means of the mounting device, when the polyethylene foam board is mounted, convenience and quickness are achieved, and the foam board is mounted and fixed in the straight and smooth state.