Grey system theory can powerfully deal with incomplete and uncertain information. In this paper, we introduced an improved grey GM(1,1) model that integrates residual modification with Markov chain model. By this model, we improved the forecast accuracy of original grey forecast model and achieved the predictions and analyses of GDP, Population and Energy consumption of Iran from 2009 to 2021 Based on the data from 1992 to 2006. We examined development relationship between GDP, Population and Energy consumption in the future.