In neighborhood rough set theory, traditional heuristic algorithm for computing reducts does not take the stability of the selected attributes into account, it follows that the performances of the reducts may not be good enough if the perturbations of data occur. To fill the gap, the mechanism of acquiring the most significant attribute is realized by two steps in the reduction process: firstly, several important attributes are derived in each iteration based on several radii which are close to the given radius for computing reduct; secondly, the most significant attribute is selected from them by a voting strategy. The experiments verify that such method can effectively improve the stabilities of the reducts, and it does not require too much attributes for constructing the reducts,