Anchor DMUs are a new class in the general classification of Decision Making Units (DMUs) in Data Envelopment Analysis (DEA). An anchor DMU in DEA is an extreme-efficient DMU that defines the transition from the efficient frontier to the free-disposability part of the boundary of the Production Possibility Set (PPS). In this paper, the anchor points of the PPS of the CCR model are investigated. A basic definition of anchor point based on the supporting hyperplanes of the PPS of CCR model is provided. Then, by using a variant of super-efficiency models, the necessary and sufficient conditions for a DMU to be an anchor DMU are provided via some theorems. To illustrate the applicability of the proposed model, some numerical examples are finally given.