Publishing microdata raises concerns of individual privacy. When there exist outlier records in the microdata, the distinguishability of the outliers enables their privacy to be easier to be compromised than that of regular ones. However, none of the existing anonymization techniques can provide sufficient protection to the privacy of the outliers. In this paper, we study the problem of anonymizing the microdata that contains outliers. We define the distinguishabilitybased attack by which the adversary can infer the existence of outliers as well as their private information from the anonymized microdata. To defend against the distinguishabilitybased attack, we define the plain k-anonymity as the privacy principle. Based on the definition, we categorize the outliers into two types, the ones that cannot be hidden by any plain k-anonymous group (called global outliers) and the ones that can (called local outliers). We propose the algorithm to efficiently anonymize local outliers with...