This paper proposes a novel phase estimator based on fully-traversed Discrete Fourier Transform (DFT) which takes all possible truncated DFT spectra into account such that it possesses two merits of `direct phase extraction` (namely accurate instantaneous phase information can be extracted without any correction) and suppressing spectral leakage. This paper also proves that the proposed phase estimator complies with the 2-parameter joint estimation model rather than the conventional 3-parameter joint model. Numerical results verify the above two merits and demonstrate that the proposed estimator can extract phase information from noisy multi-tone signals. Finally, real data analysis shows that fully-traversed DFT can achieve a better classification on the phase of steady-state visual evoked potential (SSVEP) brain-computer interface (BCI) than the conventional DFT estimator does. Besides, the proposed phase estimator imposes no restrictions on the relationship between the sampling rates and the stimulus frequencies, thus it is capable of wider applications in phase-coded SSVEP BCIs, when compared with the existing estimators.