Abstract We firstly combine multi-scale method (MS) and weighted-permutation entropy (WPE) to analyze chaotic, noisy, and fractal time series, and find that MSWPE can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise, a task that multi-scale permutation entropy (MSPE) fails to work. We then apply MSWPE to analyze the signals from vertical upward oil-in-water two-phase flow experiments. Our results suggest that the change rate of MSWPE enables to characterize the transition of flow patterns and multi-scale weighted-permutation entropy allows indicating the discrepancy of complexity of oil-in-water two-phase flow.