We propose a multivariate graph centrobaric trajectory-based method for characterizing nonlinear dynamics from high-dimensional chaotic time series. After the optimal selecting of the embedding dimension and time delay, we map the high-dimensional vector point into the two-dimensional radial plane graph, i.e., the high-dimensional vector point is transformed correspondingly to a geometric polygon. By extracting the geometric location of the polygon barycenters, we can obtain the evolving feature of the barycenter dynamical trajectory. Then we use the moment quantity of the barycenter trajectory to distinguish different chaotic time series. Finally, we apply our method to the fluctuating signals measured from gas-liquid two-phase flow experiments. The results suggest that our method can be a powerful tool for not only distinguishing the different flow patterns but also investigating the dynamical evolving mechanism of flow patterns.