This paper proposes an algorithm based on rounded partition function for k-anonymity. By rigorous theoretical proof, the study will show that a better upper bound on size of the anonymization groups can be obtained in non-trivial data sets. In particular, when the size of the original dataset is greater than 2k², the upper bound will be reduced to k+1. Further, the average size of all anonymization groups of the anonymous data will be close enough to k when the size of the original dataset is large enough. Experimental results on real datasets show that this algorithm is effective and feasible.