People have been or are about to take many measures to reduce greenhouse gases emissions, carbon dioxide focused, which are considered the chief culprit of global climate change. The inspection of carbon emissions is the basis of these measures. The evolutionary game relationship lies in the environmental authorities and carbon emitters, both are bounded rational. The replicated dynamics mechanism is utilized to analyze the repeated game of them. The punishment for the illegal carbon emission, the rewards and punishment to the environmental authorities and the environmental inspection cost have significant impact on the strategy choise. Increasing the punishment for illegal carbon emission, increaseing the punishment for dereliction of duty, reducing the inspection cost by promoting the new technology and adjusting the overlapping management will make the carbon emitters legitimate and the environmental authorities conscientious.