This study will demonstrate, through an econometric approach, the relationship among per capita GDP, CO2 emissions, and energy use in Vietnam. Using annual data for years 1970-2014, stationarity, structural breaks, Toda-Yamamoto test, Johansen and Juselius approach, and Variance decomposition have been conducted. The causality results in our analysis highlight that the presence of unidirectional causality was running from economic growth to energy consumption. This result will be significant since it supports the conservation hypothesis for the economy of Vietnam. Finally, the results of the variance decompositions reject the hypothesis that energy is neutral for growth, but that there is a relationship link even if the effects last for a short time.