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Presence of various types of inter-circuit faults between parallel transmission lines combined with the effect of mutual coupling and fault-resistance makes the protection of parallel transmission lines quite complicated. The authors have proposed a new adaptive digital distance relaying scheme which takes care of all the abnormalities of the conventional ground distance relays and measures the correct value of impedance during phase-to-phase and phase-to-phase-to-ground inter-circuit faults. The impact of fault-resistance and mutual coupling phenomena has been considered during such types of inter-circuit faults. The proposed adaptive scheme is based on the derivation of the compensated value of impedance using symmetrical component theory without the need of remote end data. To validate the proposed scheme, numerous computer simulations have been carried out on an existing 400 kV parallel transmission line network using MATLAB/SIMULINK software. The simulation results demonstrate the effectiveness of the proposed scheme giving an average percentage error of 0.579 . The results indicate that the proposed technique is highly accurate and robust for a wide variation in system and fault conditions.