NrnC from Agrobacterium tumefaciens (At_NrnC, UniProt accession number A9CG28) is a nuclease containing a single DEDDy domain. Here, we determined the structures of both the apo and metal-ion-bound forms of At_NrnC. Although the overall structure of the At_NrnC protomer is similar to that of the RNase D exonuclease domain, nuclease assays unexpectedly revealed that At_NrnC possesses remarkably different substrate specificity. In contrast to RNase D, which degrades both single-stranded RNA (ssRNA) and double-stranded RNA (dsRNA), At_NrnC hydrolyses ssRNA, single-stranded DNA (ssDNA), and double-stranded DNA (dsDNA) with high efficiency but does not degrade dsRNA. Crystal packing analysis and biochemical data indicated that At_NrnC forms an octameric hollow cylindrical structure that allows ssRNA, ssDNA, and dsDNA, but not dsRNA, to enter the central tunnel where the multiple active sites perform hydrolysis. This novel structural feature confers a high processivity and is responsible for the preference of At_NrnC for longer dsDNA substrates.