Rough sets, as a method of granular computing, can be used for dealing with uncertain information. Compared with classical rough sets, covering rough sets have more widely used. There are two methods for studying rough sets, namely the axiomatic and constructive methods. In this paper, based on some notions, two types of positive-negative region covering-based rough sets are investigated within an axiomatic approach. First, we define two types of positive-negative region covering-based rough sets. Moreover, some characteristics of these positive-negative region are validated. Second, the axiomatic systems of these two types of negative region are founded. Final, the conditions of axiomatic systems for characterizing negative region are independent of each other.