This paper presents an impedance differential protection scheme for a double-circuit transmission line. Current and voltage measurements at both line ends enable the formulation of a differential impedance that serves as an effective protection standard for transmission lines. The proposed method takes into consideration the effects of the line's shunt capacitance since it is based on the distributed parameter line model. The proposed protection system is able to detect the faults and also has the ability to determine the fault location. In addition, the relay offers dependability, and selectivity for differentiating between internal and external faults, thereby stays steady against external faults. The proposed method has been tested with varying fault resistances and under various fault conditions. The effectiveness, security, and dependability of the method are verified by the simulation results.