RE J1034+396, a narrow-line Seyfert 1 active galactic nucleus (AGN), is the first example of AGNs that exhibited a nearly coherent quasi-periodic oscillation (QPO) for the data collected by XMM-Newton in 2007. The spectral behaviors and timing properties of the QPO have been studied since its discovery. We present an analysis of the QPO in RE J1034+396 based on the Hilbert-Huang transform. Comparing with other time-frequency analysis methods, the Hilbert spectrum reveals the variation of the QPO period in great detail. Furthermore, the empirical mode decomposition provides bandpass-filtered data that can be used in the O-C and correlation analysis. We suggest that it is better to divide the evolution of the QPO in this observation into three epochs according to their different periodicities. In addition to the periodicities, the correlations between the QPO periods and corresponding mean count rates are also different in these three epochs. Further examining the phase lags in these epochs, we found no significant phase lags between the soft and hard X-ray bands, which is also confirmed in the QPO phase-resolved spectral analysis. Finally, we discuss the indications of current models including a spotted accretion disk, diskoseismology, and oscillation of shock according to the observed time-frequency and spectral behaviors.