Due to multiple properties, the international crude oil price is influenced by various and complex interrelated factors from different determinants in different periods. However, the previous studies on crude oil price fluctuation with economic policy uncertainty (EPU) haven’t taken a wider range of volatility sources into their analysis frameworks. In this paper, the time-varying parameter factor-augmented vector autoregressive (TVP-FAVAR) model is introduced in order to avoid important information loss, as well as capture the time-varying impact on crude oil price fluctuation by EPU. Furthermore, the differences on crude oil fluctuations from net-oil exporting and net-oil importing country’s EPU are also elaborated. Here are three findings as follows. First, the impacts of global EPU on the crude oil price volatility show time-varying characteristics both in time duration and time-points. Second, the instantaneous impacts of global EPU on the price volatility of crude oil are directly relevant to major events, and the impacts are different in event types as well. Third, the time-varying characteristics depicting the impacts of EPU in countries who are net-oil exporter and net-oil importer on price volatility of crude oil show heterogeneity in fluctuation range, fluctuation intensity, and stage.