In LDCs like Ethiopia, one of the major macroeconomic problems is the absence of effective monetary policy. The money demand function play a major role in macroeconomic analysis, especially in selecting appropriate monetary policy actions. The objective of monetary policy in the least developing countries (LDCs) is usually related to money and credit control, price stabilization and economic growth. Many LDCs considered, price stability as the most important objective of monetary polices and it is important to testing the stability of parameter of money demand function indicate the effectiveness of the conduct of monetary policy. The research to be conducted therefore is to investigate the determinants of money demand function. Based on the data, which could be found an error correction model (ECM) was applied to estimate the money demand function in Ethiopia. From the study it is found that, money demand is positively related with real GDP and it is negatively related with expected inflation. The coefficient of real effective exchange rate is positive or negative depending on the magnitude of the appreciation and depreciation of local currency. Thus the studies calls for appropriate formulation and implementation of sound monetary policy capable of bringing stability in the coomy coupled with sustainable growth. Keywords : money demand , economic growth , error correction model DOI : 10.7176/DCS/9-1-02