In recent years， mal-operation of pilot distance relay happens occasionally in multi-circuit transmission lines because of the complexity of electromagnetic coupling. The distance measure device of the relay plays a key role in fault locating. The deviation of the measured grounding impedance may be caused by influence of zero mutual inductance，and potentially lead to over or under range action of the relay. Considering the inherence of power system states and based on its various operating modes， operation condition and arrangements of multi-circuit lines， qualitative and quantitative analysis of the influence from zero mutual inductance on the measured grounding impedance is given. Furthermore， a method which configures the zero sequence current compensation factor to eliminate the measurement error of ground distance protection is also provided.