We report an anomalous dielectric effect of electrolytes under cylindrical nanoconfinement. In bulk phase, the decrease in the water dielectric constant (ε) with increasing salt concentration is well known, and is due to dielectric saturation. From molecular dynamic simulations of confined water and NaCl solutions, we show a dielectric anisotropy and an unexpected increase in ε(perpendicular) of NaCl solutions with respect to the confined pure liquid until a critical concentration is reached. We infer that this striking dielectric behavior results from the interplay between the effect of confinement and that of ions on the water hydrogen bonding network.