Voltage-current characteristics of High Temperature Superconductor(HTS) tapes after applying the current beyond their critical current was investigated. When over-current is applied, the current begins to flow through the metal sheath instead of superconductor. The HTS tapes quenched were analyzed using V-I curve with various magnitudes of current. Two kinds of tapes were compared with each other to examine the influence of critical current on quench development. As a result, it was found that the resistance of superconductors and joule heat due to the over-current affect current distribution in HTS tapes. Critical current of HTS tapes was considered as a main factor deciding over-current characteristics.