We report magnetization measurement in the superconducting state of a type-II organic layered superconductor with asymmetrical donor k-(MDT-TTF)2AuI2. The demagnetization factor of a plate-like shape of the single crystal has been taken into account for the measurement by applying an external field perpendicular to the conducting plane. The superconducting transition temperature TC is determined to be 4.7 K through the detection of demagnetization signal. The lower critical field is 10.5±1.4 G. This result implies that the stable vortex state of k-(MDT-TTF)2AuI2 can be reached at the applied magnetic field above 105 Oe