A vibration damping structure for a heat-transfer tube bundle including columns arranged at an interval and each composed of a plurality of heat-transfer tubes curved in a common plane and arranged in parallel to each other. The vibration damping structure includes a first vibration damping member and a second vibration damping member disposed between the columns so as to intersect the array direction of the columns. The first vibration damping member and the second vibration damping member are disposed at different positions in an axial direction of each heat-transfer tube, and thicknesses of the first vibration damping member and the second vibration damping member in the array direction are larger than an average value of a clearance between the columns under operation.