Connectedness is the key to modern risk measurement and management. This study investigates the international connectedness of crude oil prices and explores its time-varying characteristics based on a connectedness measurement framework using daily international crude oil prices. The international connectedness of crude oil prices is investigated from three perspectives: total connectedness, total directional connectedness, and pairwise directional connectedness. We find that the total connectedness of crude oil prices is 67.3%. We also find that the crude oil prices of Tapes, Daqing, Dubai and Minas are highly affected by Brent and WTI (West Texas Intermediate) crude oil prices. Furthermore, WTI and Brent are the price makers of international crude oil prices, while Tapes, Daqing, Dubai and Minas are price takers. From the perspective of pairwise directional connectedness, we find that the degree of pairwise directional connectedness between Brent and WTI are high. Finally, the structure of international crude oil markets stays the same even after market shocks. The main contributions of this study are identification of dynamic connectedness and presentation of the network connectedness of international crude oil prices.