We present results of new ASCA observations of the low-luminosity AGN ( LLAGN ) NGC 4579 obtained on 1998 December 18 and 28 , and we report on detection of variability of an iron K emission line . The X-ray luminosities in the 2–10 keV band for the two observations are nearly identical ( L _ { X } \approx 2 \times 10 ^ { 41 } ergs s ^ { -1 } ) , but they are \sim 35 % larger than that measured in 1995 July by Terashima et al . An Fe K emission line is detected at 6.39 \pm 0.09 keV ( source rest frame ) which is lower than the line energy 6.73 ^ { +0.13 } _ { -0.12 } keV in the 1995 observation . If we fit the Fe lines with a blend of two Gaussians centered at 6.39 keV and 6.73 keV , the intensity of the 6.7 keV line decreases , while the intensity of the 6.4 keV line increases , within an interval of 3.5 yr . This variability rules out thermal plasmas in the host galaxy as the origin of the ionized Fe line in this LLAGN . The detection and variability of the 6.4 keV line indicates that cold matter subtends a large solid angle viewed from the nucleus and that it is located within \sim 1 pc from the nucleus . It could be identified with an optically thick standard accretion disk . If this is the case , a standard accretion disk is present at the Eddington ratio of L _ { Bol } / L _ { Eddington } \sim 2 \times 10 ^ { -3 } . A broad disk-line profile is not clearly seen and the structure of the innermost part of accretion disk remains unclear .