Since a stabilizer of YBCO coated conductor (CC) plays a very important role of bypassing over-current and transferring heat generated in the moment of fault, it is one of big issues to determine the material of the stabilizer and its dimension for the high performance of the HTS power application system. Especially, in the case of a superconducting fault current limiter (SFCL), which requires it to react immediately to the occurrence of fault, characteristics of stabilizer are decisive in limiting fault current and recovering superconducting properties during and after quenching. In this paper, the quench / recovery characteristics of YBCO CCs with various thickness of stabilizer were analyzed. The quench/recovery test carried out at 20 $V_{rms}$, 5 cycles (60 Hz) and results showed that as the thickness of the stabilizer decreased, both the final approach temperature and the recovery time decreased.