In order to analyze the complex phase transition in the gas-liquid-solid three-phase mixing systems and to predict gas-liquid-solid multiphase mixing time, a novel method combined image processing technology, computational homology and CFD (Computational Fluid Dynamics) numerical simulation is introduced in this study. Firstly, the volume of fluid (VOF) multiphase flow model in FLUENT software is used for the simulation of fluid characteristics. Secondly the patterns produced by phase transition in the stirred tank are binaryzed. Finally evolution profile of the zeroth dimensional Betti numbers and the first dimensional Betti numbers in time series are obtained separately. In fact,some aggregates still remain in the tank after the homogeneous mixing.Comparing with the fractal method to characterize the mixing time, the result shows that this method not only can predict the gas-liquid-solid mixing time by the zeroth dimenstional Betti numbers, but also can predict the amount of these aggregates in the stired tank by the first dimenstional Betti numbers, leading to a useful parameter to characterize the non-uniformity of gas-liquid-solid mixing.