Classic coherence analysis has been commonly used as a effective method for the analysis of stationary signals. To study the instantaneous coherence between non-stationary signals, we extended the concept of coherence to time-varying coherence using some time-frequency analysis methods. Wavelet-based coherence is one of the most widely used time-varying coherence methods, but few researchers have applied Hilbert-Huang transform (HHT) to coherence analysis, which also has excellent characteristics of time-frequency analysis. Therefore, this paper proposed the concept of HHT coherence, derived its method based on wavelet coherence and verified its feasibility. Then, we compared wavelet coherence and HHT coherence from three different aspects: the time-frequency resolution, effects of noise and adaptivity. The results of different simulating signals demonstrated that HHT coherence had higher time resolution, frequency resolution and more adaptivity than wavelet coherence under ideal conditions. However, due to its imperfect algorithm, the time-frequency resolution of HHT coherence was reduced by the effect of mode mixing, boundary distortion and noise. By contrast, wavelet coherence is more stable.