Measurements of the complex impedance of a single crystal of Ag beta-alumina have been made in the frequency range of 1 Hz-10(6) Hz. Ag beta-alumina is an ideal two-dimensional superionic conductor (SIC). The slope of AC conductivity sigma(omega) was investigated in the temperature range from approximately 100 K to room temperature. A small power-law dependence sigma(omega) infinity omega(s) was found, with the slopes being evaluated as 0.11-0.15. In the present study, a "scale-invariance" for SIC with a two-dimensional disordered system was suggested from the small power-law dependence. (C) 2013 Elsevier B.V. All rights reserved.