In two dimensions, the \beta-skeleton is one of the most practical methods for reconstructing smooth curves from a given unorganized point set because of its provable guarantee. In three dimensions, however, the \beta-skeleton cannot be used for surface reconstruction because it may contain unwanted holes omnipresently, no matter how high sampling density is. To overcome this difficulty, an extension of the \beta-skeleton, called greedy \beta-skeleton, is proposed. It is shown by computational experiments that the unwanted holes do not appear in the greedy \beta-skeleton even when the dimension is three. In addition, the greedy \beta-skeletons are computed for several practical inputs, and their fairness is examined. Computation results for some variants of the greedy \beta-skeleton are also reported.