The magnetic torque and high-pressure transport properties of the incommensurate organic superconductor (MDT-TS)(AuI_2_)_0.441_ are investigated, where MDT-TS is 5H-2- 1,3-diselenol-2-ylidene -1,3,4,6-
tetrathiapentalene. The magnetic torque provides unquestionable evidence of an antiferromagnetic ordered
state with a high spin-flop field of 6.9 T at ambient pressure. Hydrostatic pressure suppresses this insulating
state and induces superconductivity, where the superconducting transition temperature rises to the maximum,
4.9 K at 1.27 GPa; the superconducting phase exists between 1.0 and 1.8 GPa above 1.5 K.