A sound absorption block installed at a music box, a gymnasium, a studio, etc. to prevent sounds from being heard outside, and a method of constructing the same are disclosed. The present invention provides a sound absorption block, including a lower plate where a plurality of unit structures are regularly arranged in horizontal and vertical directions, the unit structure having rectangular an opening that becomes gradually smaller; and an upper plate arranged on the lower plate to divide each of the openings of the unit structures in four parts. Accordingly, the sound absorption block of the present invention may be made of metals, as well as inexpensive building residues, etc. because a sound wave was decreased and offset regardless of the materials.