In this work, we develop a field-effect transistor with a two-dimensional channel made of a single graphene layer to achieve label-free detection of DNA hybridization down to attomolar concentration, while being able to discriminate a single nucleotide polymorphism (SNP). The SNP-level target specificity is achieved by immobilization of probe DNA on the graphene surface through a pyrene-derivative heterobifunctional linker. Biorecognition events result in a positive gate voltage shift of the graphene charge neutrality point. The graphene transistor biosensor displays a sensitivity of 24 mV/dec with a detection limit of 25 aM: the lowest target DNA concentration for which the sensor can discriminate between a perfect-match target sequence and SNP-containing one.