Human DNA polymerase kappa (Pol kappa) is a proficient extender of mispaired primer termini on undamaged DNAs and is implicated in the extension step of lesion bypass. We present here the structure of Pol kappa catalytic core in ternary complex with DNA and an incoming nucleotide. The structure reveals encirclement of the DNA by a unique "N-clasp" at the N terminus of Pol kappa, which augments the conventional right-handed grip on the DNA by the palm, fingers, and thumb domains and the PAD and provides additional thermodynamic stability. The structure also reveals an active-site cleft that is constrained by the close apposition of the N-clasp and the fingers domain, and therefore can accommodate only a single Watson-Crick base pair. Together, DNA encirclement and other structural features help explain Pol kappa's ability to extend mismatches and to promote replication through various minor groove DNA lesions, by extending from the nucleotide incorporated opposite the lesion by another polymerase.