We fabricated an a-IGZO thin film transistor (TFT) with AZO/Ag/AZO transparent multilayer source/drain contacts by rf magnetron sputtering. a-IGZO TFT with AZO/Ag/AZO multilayer S/D electrodes (W/L = 400/50 ${mu}m$) showed a subs-threshold swing of 3.78 V/dec, a minimum off-current of $10^{-12}$ A, a threshold voltage of 0.41 V, a field effect mobility of $10.86cm^2/Vs$, and an on/off ratio of $9{ imes}10^9$. From the ultraviolet photoemission spectroscopy, it was revealed that the enhanced electrical performance resulted from the lowering of the Schottky barrier between a-IGZO and Ag due to the insertion of an AZO layer and thus the AZO/Ag/AZO multilayer would be very appropriate for a promising S/D contact material for the fabrication of high performance TFTs.