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The uncontrolled climate change is one of the most significant threats to the sustainable development of the human societies. Since the establishment of the Kyoto Protocol in 1997, several models have been proposed to limit the emission of Greenhouse Gases (GHGs) by trying to enforce abiding regulations to the participating countries. One of the successful implementations of such models is the Emission Trading System in the European Union, which economically incentivizes the carbon-heavy industries to cut their emissions on a gradual basis. In this paper, we have modeled the involving factors in such a carbon market through the system dynamics methodology, proposing a system of differential equations between the main factors such as the Emission Allowances supply, demand and their price. The coefficients are derived based on a Least Absolute Deviation (LAD) analysis on the historic available data. We analyze the effect of an implementable policy and show that by consistently increasing the coverage of the emissions from industries, the EU commission can reach to its predefined set values of the allowable volumes of emissions by 2050.