An organic salt, -͑BEDT-TTF͒ 4 Hg 2.89 Br 8 exhibits superconductivity at 4.3 K under ambient pressure suggesting non-Fermi-liquid ͑NFL͒ behavior just above T c . Whereas most organic superconductors are controlled by the bandwidth in the half-filled electron system, this salt realizes a carrier doping away from the half-filled electron system as well as high-T c cuprates. In order to investigate the origin of NFL behavior, we assessed 13 C-NMR measurements in this salt and observed the antiferromagnetic fluctuation as same as in an organic antiferromagnet -͑BEDT-TTF͒ 2 Cu͓N͑CN͒ 2 ͔Cl with the gap structure. Application of pressure suppresses ͑T 1 T͒ −1 and shifts its maximum to lower temperatures with ͑T 1 T͒ −1 becoming constant above 2 GPa. These results suggest that applying pressure alters the electron system from NFL to FL state and that antiferromagnetic fluctuations contribute to the origin of NFL behavior. The physics of organic conductors involve a strongly correlated electron system, similar to that of high-T c cuprates and heavy-fermion systems.1 For example, bis͑ethylenedithio͒-tetrathiafulvalene ͑BEDT-TTF͒, together with inorganic ions, forms many conducting salts, which have various crystal structures. Although the conducting layers of all of these salts consist of the same molecule, these salts show a variety of behavior, from superconductivity to high-resistance insulator.2 These salts can also be classified by the arrangement of their BEDT-TTF molecules with the arrangement and the electronic properties being closely related. In -͑BEDT-TTF͒ 2 X, two BEDT-TTF molecules form a dimer and constitute a two-dimensional conducting sheet, with one electron per dimer.3 Hence -͑BEDT-TTF͒ 2 X is regarded as a two-dimensional half-filled electron system. Many -͑BEDT-TTF͒ 2 X salts act as superconductors with the superconducting and antiferromagnetic insulating phases being adjacent to or coexisting at low temperatures. 5,6 Therefore, these salts are ideal for investigating the relationship between superconductivity and antiferromagnetism.Carrier doping and applying pressure are complementary methods for research on the phase diagram. Whereas high-T c cuprates showed superconductivity after carrier doping, many organic superconductors showed superconductivity after applying pressure.7 Cuprates and -͑BEDT-TTF͒ 2 X show both similarities and dissimilarities. Despite differences in their ionic and molecular crystals, cuprates and -͑BEDT-TTF͒ 2 X have similar properties, in that their superconductive and antiferromagnetic phases are neighboring, and the order parameter of the superconductivity has d-wave symmetry.8-13 Just above T c , -type salts show Fermi-liquid ͑FL͒ behavior, as shown by their conductivity, spin susceptibility and ͑T 1 T͒ −1 , 5,14,15 whereas high-T c cuprates show non-Fermi-liquid ͑NFL͒ behavior just above T c . To investigate the origin of those similarities and dissimilarities, it is important to assess the material that connects cuprates and -͑BEDT-TTF͒ 2 X. Since carrier doping to organ...