From the perspective of global economic general equilibrium, this study developed a new climate change IAM named CIECIA. The economic core of this IAM is a multi-country-sector general equilibrium model. The endogenous technology progress mode is introduced into CIECIA. Based on this model, three assessment principles of the global cooperating abatement scheme are proposed, including effectiveness, feasibility, and fairness. This study simulated and analyzed six types of primary global cooperating abatement schemes. The simulated results indicate that all of the selected schemes can satisfy the climate mitigation targets by 2100. Thus, they are all effective schemes. However, the schemes have quite different feasibilities and fairness. The Stern Scheme benefits the developed countries, but is unfair to the developing countries. The Nordhaus Scheme promotes the developments of the developing countries. However, it leads to negative impacts on the interests of the developed countries. The principle of convergence on accumulated carbon emissions per capita and the principle of convergence on carbon emissions per capita benefit the economic developments of the middle and low developing countries most. However, these two types of schemes cause tremendous losses to the main economic entities in the world including China. The Pareto Improvement Scheme, which was developed from the Global Economic Growth Scheme, balances the fairness and feasibility in the carbon abatement process and realizes the Pareto improvement of accumulated utilities in all the participating countries. Thus, the Pareto Improvement Scheme is the most reasonable global cooperating carbon abatement scheme.