Differently from BSCCO tapes which are fabricated by powder-in-tube method, the coated conductors are made by the evaporation of YBCO on metal substrate. Due to this structural merit, although the coated conductors are generally used for large current transportation, they are expected to be favorable to the purpose of the fault current limitation as well. In this study, using YBCO coated conductor having copper stabilizer formed by plating technique(produced by Superpower Co.), we investigated the over-current characteristics of the coated conductor. The coated conductors had 85 A $I_c$ and 90 K $T_c$. The resistance of the conductor was 0.93 $m{Omega}/cm$ at 300 K and 0.17 $m{Omega}/cm$ at the temperature right above $T_c$. To the coated conductors, we applied the voltages of the range from 150 $V_{rms}$ to 230 $V_{rms}$ and measured the V-I curves using four probe method. From the results, we could analyze the electric behavior of the coated conductor in flux flow state. As the current exceed $I_c$, the currents were distributed into the superconductor and metal stabilizer. The amounts of the currents shared through both current paths were calculated under the assumption that the ,Joule heating was perfectly eliminated by $LN_2$ surrounding the conductor. Finally, the condition for the stable current flowing state which does not affect the conductor was established from the analysis on the over-current characteristics.