Abstruct Economic growth is one of the most powerful measurement for eliminating poverty and improving the quality of life satndards in developing countries. The objective of this study is used to investigate the relationship among some economic growth indicator variables such as RGDP, inflation rate and unemployment rate using multivariate time series approch for the anually data that was obtained from the national bank of Ethiopia and World Bank website statistical bulletin for the period 1983-2017. This study used the most popular method of ADF and PP unit root test for stationarity test of RGDP, inflation rate and unemployment rate in this study Differencing used for transform non-stationary time series to stationary time series. The cointegration analysis is used to determine the long run relationship and VECM used to determine the short run relationship among economic indicators in Ethiopia. Here also Johensen cointegration test methodology was used to determine the number of cointegrating equation. In the same way structural VAR such as Granger causality test was used to check for direction of causal relationship among the variables either unidirectional or bidirectional and feedback. On the other hand Inpulse response function indicate the effects of an exogenous shock on the whole process over time and FEVDs tells us the prroportion of movements in sequence due to its shocking innovations versus shocks to other variables and it shows that the portion of the variance in the forecast error for each variable due to innovations to all variables in the system. There is long run relationship based on Johansson Cointegration test and short run relationship based on VECM among economic growth indicator variables and the VECM is appropriate than VAR model infers that the current real economic growth of Ethiopia. Granger causality shows unidirectionally the change in consumer price index(inflation) and unemployment leads to changes to real GDP growth and unidirectionally from UR to CPI which shows that unemployment leads to change of inflation. Empirical results of impulse response function analysis show that shock to RGDP leads to negative response from unemployment which dies out after four years horizons, while the shock to RGDP from inflation of goods and services produces continuous positive responses.The FEVDs test results indicate that most of the variance in each variable is attributable or explained by own shocks at first and second horizon. Key words: Economic growth,Unemployment rate, Inflation rate,VECM,VAR, cointegration and FEVDs