This paper proposes a new Fourier transform-based phasor estimation method to eliminate the adverse influence of the exponentially decaying dc offsets when Discrete Fourier Transform (DFT) is used to calculate the phasor of the fundamental frequency component in a relaying signal. By subtracting the result of odd-sample-set DFT from the result of even-sample-set DFT, the information of dc offsets can be obtained. Two dc offsets in a relaying signal are treated as one dc offset which is piecewise approximated in one cycle data window. The effect of the dc offsets can be eliminated by the approximated dc offset. The performance of the proposed algorithm is evaluated by using computer-simulated signals and EMTP-generated signals. The algorithm is also tested on a hardware board with TMS320C32 microprocessor. The evaluation results indicate that the proposed algorithm has the stable and accurate eliminating performance even if the input signal contains two decaying dc components having different time constants.