A clustering algorithm named “Clustering by fast search and find of density peaks” is for finding the centers of clusters quickly. Its accuracy excessively depended on the threshold, and no efficient way was given to select its suitable value, i.e., the value was suggested be estimated on the basis of empirical experience. A new way is proposed to automatically extract the optimal value of threshold by using the potential entropy of data field from the original dataset. For any dataset to be clustered, the threshold can be calculated from the dataset objectively instead of empirical estimation. The results of comparative experiments have shown the algorithm with the threshold from data field can get better clustering results than with the threshold from empirical experience.