The quantitative co-relationships between the time series of Liquid Natural Gas (LNG) CIF (Cost, Insurance and Freight) prices and those of crude oil prices were estimated for Japan, EU and USA based on the monthly price data in the time period from early of 1998 to 2006 of the three regional markets. Since both prices of LNG CIF and crude oil appear to be non-stationary, the cointegration and the Error Correction Model (ECM) techniques were applied to obtain the long-run elasticity coefficients between both prices of LNG CIF and crude oil for these three markets. The obtained results suggest that 100 percent changes of the crude oil prices of Japan, EU and USA have 49 percent, 76 percent and 96 percent impacts on the respective LNG CIF prices in a long term when the crude oil price in a relative high era. The obtained long-run elasticity coefficients can be used to explain the different price changes of LNG CIF in each market with responding to dramatically changing high crude oil price in recent years.