Abstract: The problem of estimating the phase delay between two real sinusoids with unknown frequency is discussed. It is indicated that the negative frequency contribution is the essential and internal cause of the bias brought by the Discrete-time Fourier Transform (DTFT)-based phase delay estimator for real signals, when the sinusoidal frequency is quite low or close to the Nyquist frequency. Based on the DTFT-based estimator, a simple unbiased phase delay estimator with negative frequency contribution considered, is proposed for real signals with unknown frequency. The new formula for phase delay calculation is derived and detailed steps of the proposed estimator are presented accordingly. Simulation results show that the proposed estimator has removed the bias of the DTFT-based one and can attain optimum performance even when the sinusoidal frequency is quite low or close to the Nyquist frequency. Furthermore, the proposed estimator is proved to be particularly effective when there are not enough sampled data available for DTFT calculation. So the estimator is expected to be helpful to those engaged in phase/time delay estimation for many areas such as radar, machinery fault diagnosis and industrial measurement.