We investigate the dynamic characteristics of vertical upward water-dominant oil-water two-phase flow by multiscale permutation entropy algorithm. We first measure the two-phase flow conductance fluctuation signals in a 20 mm inner-diameter pipe. Then we calculate the multiscale permutation entropies for different water-dominant flow patterns. The results indicate that multiscale permutation entropy rate and average of mutiscale permutation entropy can be used as quantitative parameters for measuring complexity of water dominant oil-water two-phase flow. In addition, we propose a new approach to identify different water-dominant flow patterns by using the joint distribution of multiscale permutation entropy rate and cumulant of increment series.