The model of Vector Autoregressive (VAR) with cointegration is able to be modified by Vector Error Correction Model (VECM). Because of its simpilicity and less restrictions the VECM is applied in many studies. The correlation among variables of multivariate time series also can be explained by VECM model, which can explain the effect of a variable or set of variables on others using Granger Causality, Impulse Response Function (IRF), and Forecasting. In this study, the relationship of Energy Used and CO2 will be discussed. The data used here were collected over the year 1971 to 2018. Based on the comparison of some criteria: Akaike Information Criterion Corrected (AICC), Hannan-Quin Information Criterion (HQC), Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC) for some VAR(p) model with p= 1,2,3,4,5, the best model with smallest values of AICC, HQC, AIC and SBC is at lag 2 (p= 2). Then the best model found is VECM (2) and further analysis such as Granger Causality, IRF, and Forecasting will be based on this model.