We report molecular dynamics (MD) simulations of the reverse translocation of single nucleotides through a narrow carbon nanotube (CNT), with a diameter of 1.36 nm, immersed in a 1 M KCl electrolyte solution under an applied electric field along the tube axis. We observe ion selectivity by the narrow CNT, which leads to a high flow of ions, in contrast to a negligible and opposing current of Cl- ions. The ions, driven by the electric field, force a negatively charged single nucleotide into the narrow CNT where it is trapped by the incoming K+ ions and water molecules, and the nucleotide is driven in the same direction as the K+ ions. This illustrates a novel mechanism of nucleotide reverse translocation that is controlled by ion selectivity. An increase in the CNT diameter to 2.71 nm or an increase in nucleotide chain length both lead to translocation in the normal direction of the applied field. The reverse translocation rate of single nucleotides is correlated to the ionic current of K+ ions in the narrow tube, unlike translocation in the normal direction in the wider tube.