The study explores the characteristics of non-linear fluidization of vibration gas-solid fluidized bed (VGFB) and the laws of wave energy transfer. A VGFB (phi 110 mm x 180 mm) with the -0.3 + 0.074 mm magnetite particle was adopted in the experiment. The Hilbert-Huang transform (HHT) analysis of the pressure signal was used to obtain the time-frequency-energy two-dimensional Hilbert-Huang spectrum of pressure fluctuation signals under different fluidized states, and this revealed that the pressure fluctuation signal was composed of complex inter- and intra-wave frequency modulation components, this verified the non-linearity and randomness of the pressure signal. The distribution of the empirical mode decompositions (IMFs) energy of pressure fluctuation signal under different operation conditions was analyzed, and the results indicated that the IMF4 energy increased with increases in the bubble size. Conversely, with decreases in the bubble size, the energy was gradually transferred from IMF4 to IMF3, this revealed that the energy distribution of IMF3 and IMF4 exhibited a good correspondence with the bubble phase behavior and was a quantitative reflection of the non-linear bed fluidization. Finally, the main frequency and energy of the pressure signal were used to describe the dynamic behavior of the VGFB under different fluidized states. The results indicated that the pressure fluctuation frequency of quasi-dispersive fluidization and bubbling fluidization were both lower than that of the frequency of turbulent fluidization. Additionally, the pressure signal energy of quasi-dispersive fluidization was the lowest, bubbling fluidization was intermediary, and turbulent fluidization was the highest. (C) 2018 Elsevier B.V. All rights reserved.