We build a continuous-time stochastic real options model to study the abandonment strategy of carbon capture and storage (CCS) project. Based on the stochastic optimal control theory, we solve the problem with the Hamilton-Jacobi-Bellman variational inequality (HJBVI) to derive the evolution of the optimal CCS investment over time. Using optimal stopping time, we establish a free boundary for each time node over the entire CCS construction stage as a function of the market carbon price and the individual project's remaining total deployment investment. The boundary is to help the investors decide whether to keep investing or abandon the project. Numerical simulations based on Chinese data are conducted by applying the finite element method with the power penalty. Concerning a hypothetical CCS project with a remaining total deployment investment of 10 billion RMB, our projected critical carbon prices relevant to its decisions on CCS project in 2020 are, respectively, 137.27 RMB/ton CO2 (0.123 RMB/kW·h) and 104.14 RMB/ton CO2 (0.093 RMB/kW·h). Being well below either threshold, if the current price prevails in 2020, the private investors will have no incentive to keep investing in or operate the above CCS project. It seems to us that this should indicate the exact right moment for the government to consider subsidizing them with at least the amount of money to prevent their abandonment of CCS from happening.