The time-varying cross-spectrum method has been used to effectively study transient and dynamic brain functional connectivity between non-stationary electroencephalography (EEG) signals. Wavelet-based cross-spectrum is one of the most widely implemented methods, but it is limited by the spectral leakage caused by the finite length of the basic function that impacts the time and frequency resolutions. This paper proposes a new time-frequency brain functional connectivity analysis framework to track the non-stationary association of two EEG signals based on a Revised Hilbert-Huang Transform (RHHT). The framework can estimate the cross-spectrum of decomposed components of EEG, followed by a surrogate significance test. The results of two simulation examples demonstrate that, within a certain statistical confidence level, the proposed framework outperforms the wavelet-based method in terms of accuracy and time-frequency resolution. A case study on classifying epileptic patients and healthy controls using interictal seizure-free EEG data is also presented. The result suggests that the proposed method has the potential to better differentiate these two groups benefiting from the enhanced measure of dynamic time-frequency association.