Qatar is currently the highest emitter per capita and targets emission reduction by exercising tight controls on gas flaring. In order to limit the emission under allowances, the power plants have two options: investing in carbon capture and storage (CCS) systems or buying carbon credits for the excess emissions above their allowances. However, CCS systems are expensive for installation and operation. In this paper, a mixed integer linear programming (MILP) model is developed for the design of integrated carbon capture, transport and storage infrastructure in Qatar under carbon trading scheme. We first investigate the critical carbon credit prices to decide under which price it is more beneficial to invest on CCS systems or to buy carbon credits via carbon trading. Then the fair design of the CCS infrastructure is obtained under two fairness scenarios: the same saving ratio and the game theory Nash approach. Fair cost distribution among power plants in Qatar is obtained by selecting the CO2 resources (power plants) to be captured with available capture technologies and materials, designing the transportation pipeline network to connect the resources with the sequestration and/or utilisation sites and determining the carbon trading price and amount among power plants. Under different fairness scenarios, the total costs are slightly higher than that from minimising the total cost to obtain the fair cost distribution. Power plants with higher CO2 emissions determine to install CCS system, while other power plants buy the carbon credits from domestic or international market to fulfil their carbon allowance requirements. The future work includes extending the current model by considering power generation distribution and designing the pipeline network with the selection of pump locations and pipe diameters.