Power system has recently used Double-circuit Line and Multi-circuit Line in the industrial development. This has an advantage of system stability and reliability, but the complexity of the system has a disadvantage that makes it difficult to protect the power line. Double-circuit Line has two operation conditions in the Single-circuit operation and Double-circuit operation, so it has mutual impedance. To make it possible for the remaining single-line to operate independently while there is a fault with first line or when maintenance is needed, a trip region for the single-circuit operation should be set in order to set the relay trip region. An optimal trip region for each operation, a different operational conditions for the relay setting should be calculated. In this paper, trip regions of each operation condition have been compared by considering mutual impedance and fault resistance that led to the calculation of fault impedance. Also, as we know that one of the advantages in the distance relay is the back-up protection, we calculated the trip region(Zone-2) in consideration of the mutual impedance.