When a single-phase fault occurs on shunt reactor compensated EHV transmission lines， the elements， which compose the recovery voltage of the opened phase after the breaker tripping， include one more resonant component under transient faults than under permanent faults， so the fault nature can be distinguished by making an integral of the recovery voltage during a fundamental frequency cycle. The criterion is simple and convenient for implementation， and it has high sensitivity. It obtains results fast， which effectively solves the problem that the fault detection time is too long using the current criterions. Simulation results prove the correctness of the proposed algorithm.