Electrical conduction in $SrZr_{1-x}Y_xO_{3-delta}$((x=0.05, 0.10)-metal electrode system was investigated by impedance spectroscopy and two-probe d.c. conductivity measurement. Electrode conductivity in anodic direction varies with $P_W^{1/2}$( and that in cathodic direction with $P_{O2}^{1/4}$ in oxidizing atmosphere. In hydrogen atmosphere, the addition of water vapor increased the electrode conductivity both in anodic and cathodic direction. Increasing dopant concentration from 5 to 10% showed a more than four times increase in anodic conduction as well as bulk conduction of the solid electrolyte. This observation implies that unfilled oxygen vacancy concentration increases rapidly as the dopant content increases in humid atmosphere. The activation energy of cathodic conduction in Pt and Ag electrode was nearly same below $800^{circ}C$ which means the rate of cathodic reaction is determined by the reaction in the electrolyte surface rather than on the metal electrodes.