The electrical capacitance tomography (ECT) velocimetry techniques, namely tomography tracking velocimetry (TTV) and tomography image velocimetry (TIV) are proposed in this study to quantify the flow structure of gas-liquid-solid fluidized beds based on the ECT images. The tomography images of the bubbles in the three-phase system are obtained from image reconstruction using the neural network multi-criteria optimization image reconstruction technique (NN-MOIRT), developed earlier by the authors. The TTV is based on an auto-correlation of tomography images in a single plane sensor to track the three-dimensional,position of a bubble swarm. The TIV is based on a cross-correlation of tomography images in two plane sensors to calculate the three-dimensional velocity components of the bubble swarm. The bubble spiral motions, the fluctuations of the three-dimensional bubble swarm velocity components and fluxes in three-dimensional space are discussed along with the effect of gas superficial velocity, the presence of solid particles and the column height.