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As we know the development of one country passes through a large production of energy, more a country is developed more his appetite on energy is huge.And more a country is in shortage of energy, more his development is slowed down.That is why Cameroon as being a medium developing country aspires to become an emergent country by 2035.But at present Cameroon faced of shortage of electricity and this situation has a bad effect on the economic growth.A proper analysis and research on electricity consumption have an important impact on the government management policies or in the decision of the investors.Unfortunately Cameroon doesnt have yet an update data about electricity consumption since 2012.In this paper based on statistics, mathematics and economics theories; also on the basis of previous studies, we tried to estimate and to forecast the electricity consumption in Cameroon to help government, investors, scholars, etc.to have a tool on the electricity consumption in Cameroon since 2012.We firstly brought out the basic knowledge of Cameroon economic and the situation of electricity consumption in Cameroon; and also brought out the function of our research.Secondly we described the Grey theory model GM (1,1) and talk about the principle of Markov based on classification and decomposition of states.And we also explained how to construct the Grey-Markov model.Thirdly based on data from 2002 to 2012 we simulated the forecasting of the electricity consumption in Cameroon using Grey theory model GM (1,1) and Grey-Markov model.The simulated result shows that the precision is obviously superior using Grey-Markov model than using Grey theory model GM (1,1).So we used Grey-Markov model to estimate 2013 and .2014 electricity consumption in Cameroon and to forecast 2015 and 2016 electricity consumption in Cameroon.At the end we can formulate at relevant departments of Cameroon government the related policy to ensure the supply of electricity in Cameroon for the next oncoming years for the sustainable and ongoing development of population.