To provide a variant-can by performing a diameter-reduction process up to the vicinity of a bottom part on a trunk part of a can-body made of metal. A diameter-reduction apparatus for can-trunk for performing a diameter-reduction process on a trunk part of a can-body having a closed-end cylindrical shape with an open end, including: a can-body holder holding a bottom part of the can-body, which is provided with: a base pad abutting on the bottom part of the can-boy; and a first clamping-ring having substantially a cylindrical shape which clamps an outer circumference surface of a trunk part of the can-body at the bottom side and which moves back and forth relative to the base pad along a can-axis direction; a die unit for diameter-reduction provided with a die for a diameter-reduction process of the trunk part by moving back and forth with respect to the can-body holder along the can-axis direction; and a first clamping-ring moving device moving the first clamping-ring backward along the can-axis direction along with an advance of the die.