In this paper, we focus on the study of covering based rough sets in covering approximation spaces. Firstly, two pairs of covering approximation operators are reviewed, their properties are investigated. Secondly, Based on the covering of the covering approximation space, two new coverings of the universe are induced, by which two new pairs of covering approximation operators are constructed. Furthermore, the properties of these operators are examined. Finally, by a comparison of these approximation operators, some conditions are gained under which some or all of these approximation operators are equivalent.