Given the urgency of climate change, many countries have set carbon neutrality targets and adopted cap-and-trade (C&T) systems to regulate carbon emissions. Accurate carbon emission data is crucial for the effective operation of carbon pricing and management systems. Monitoring, Reporting, and Verification (MRV) system is at the core of these systems, facing challenges such as, inefficient verification process, and low-quality carbon emissions verification. Blockchain and smart contracts offer promising solutions to some difficulties, while the quality of carbon emissions verification still needs improvement. Therefore, we propose a blockchain-enhanced carbon emissions verification model to optimize system efficiency and support compliance verification. We employ reputation as the admission criterion, screening reliable and trustworthy verification candidates. We design a game-theoretic incentive mechanism implemented through smart contracts to promote compliance and collaborative quality control among participants. Analysis shows that our scheme drives the game model towards the Nash equilibrium that achieves collaborative quality control. Through security analysis and simulation experiments, we verify the efficacy of our mechanism concerning verification quality and procedural automation, confirming its potential to mitigate malpractices and enhance consistent compliance.