In this paper a new method for estimation and removal of decaying dc offset from fault current signal using Least Median of Squares Regression (LMSR) method is proposed. Fault currents tend to include a dc decaying component. This component decreases the accuracy and speed of the protective relaying operation. The proposed method can estimate and eliminate the dc decaying component from fault current signals after one cycle from the fault instant. The dc decaying magnitude and time constant are estimated exactly during one cycle. The dc decaying component is eliminated by subtracting the dc value at each sampling instant. To verify the performance of the proposed method, we performed a dc component estimation test and distance protection test using PSCAD/EMTDC. The results of the PSCAD/EMTDC simulation showed that the proposed method can estimate dc components exactly from fault currents and can be applied to digital protection relays for phasor extraction