A study was carried out to determine what happens with gravity around a 3-brane of a specific structure in 6D spacetime with a negative cosmological constant. It was shown that there is a normalizible graviton zero mode attached to the stringlike defect, and the contribution of bulk gravitons is suppressed, leading to O(1/r3) violations of Newton's law. A hierarchy between the four-dimensional Planck scale and the Planck scale in 6D was derived.