A high speed digital distance relaying algorithm based on a least square error method is proposed. To obtain stable phasor values very quickly, first, a lowpass filter which has very short transient period and no overshoot is presented. Secondly, the least square error method having the data window of 3 samples is used by applying a FIR filter which removes the DC-offset component in current relaying signals. Test results show that the proposed distance relaying algorithm detects most of internal faults within a half cycle after faults in a 154[kV] overhead transmission line system.