Abstract In recent years, power system uncertainties have increased due to the growing integrations of intermittent renewable energy resources. It is imperative to introduce probabilistic load flow analysis in the study of power system operation and planning to adapt to the ever-increasing uncertainties. This paper proposes a scenario-based analytical method for the probabilistic load flow analysis, which takes advantage of both the scenario analysis method and the cumulant method. This method can not only consider various kinds of correlations among power inputs but also accurately represent the probability distributions of desired outputs with a reasonable computational burden. The performance of this method is evaluated on the IEEE 14-bus and 118-bus test systems. The accuracy and efficiency of the proposed method are validated through quantitative and graphical comparisons with Monte-Carlo simulation.