Under the impact of parallel lines with magnetically strong and electrically weak connection，the false tripping of the league zero-sequence directional protection happens when ground faults occur on another line of the parallel lines.The current solution methodologies are analyzed.This problem is caused by the zero-sequence mutual potential between two lines.This can be solved by using polar voltages which do not contain zero-sequence mutual in zero-sequence directional protection.Based on this principle，two novel methods of zero-sequence directional protection are proposed using non-fault phase voltage difference ae well as zero-sequence voltage and fault phase voltage difference，thus the zero-sequence directional protection criteria are formed without the impact of zero-sequence mutual inductance.The feasibility of new zero-sequence directional protection schemes are verified by PSCAD/EMTDC simulations.