We develop a continuous-time model in which an ESG investor hires a manager to run a project and incentivizes the manager to fulfill ESG responsibilities. The manager’s private efforts and ESG investing determine the project’s cash flow and ESG performance subject to random shocks. We derive the optimal contract and its implementation after introducing carbon credits following the cap-and-trade program in practice. We provide comparative static analysis and empirical implications. The results demonstrate that ESG investing enhances contract efficiency. The more significant the carbon emission reduction, or the less the cost of ESG investing, the higher the contract efficiency, the average q, the marginal q, and the optimal investment–capital ratios, implying that ESG investing mitigates inefficiencies arising from information asymmetry and enhances investment values. Our model predictions are partially verified by empirical facts.