Global climate change is one of the most serious challenges facing humanity today. Most countries agreed that the global average temperature rising has to be controlled into 2° C compared to preindustrial world. Emission Trading Scheme is considered an effective means to achieve this goal. The essence of the scheme is the circulation of carbon emission rights. Who owns carbon emission rights? What types of carbon emission rights do countries own? How to allocate carbon emission rights? The answers of these questions form the basis of the regulation and protection of Emission Trading Scheme. From legal theory and new institutional economics, the paper discusses ownership issues of carbon emission rights. It contains not only theoretical analysis on relevant international laws and environmental laws, but also case analysis on the effect of rights allocation on transaction cost. It shows that individuals and the country share carbon emission rights. It also shows that the transaction costs may increase if the rights are allocated depends on civil law theory or emission amount. And legal institutions should endow the rights to parties with more members, looser organisation and less information, to ensure transactions go more smoothly.