In this paper, we propose a distance relaying algorithm using a Discrete Fourier Transform (DFT)-based modified phasor estimation method to eliminate the adverse influence of exponentially decaying DC offsets. Most distance relays are based on estimating phasors of the voltage and current signals. A DFT is generally used to calculate the phasor of the fundamental frequency component in digital protective relays. However, the output of the DFT contains an error due to exponentially decaying DC offsets. For this reason, distance relays have a tendency to over-reach or under-reach in the presence of DC offset components in a fault current. Therefore, the decaying DC components should be taken into consideration when calculating the phasor of the fundamental frequency component of a relaying signal. The error due to DC offsets in a DFT is calculated and eliminated using the outputs of an even-sample-set DFT and an odd-sample-set DFT, so that the phasor of the fundamental component can be accurately estimated. The performance of the proposed algorithm is evaluated for a-phase to ground faults on a 345 kV, 50 km, simple overhead transmission line. The Electromagnetic Transient Program (EMTP) is used to generate fault signals. The evaluation results indicate that adopting the proposed algorithm in distance relays can effectively suppress the adverse influence of DC offsets.