Increasing demand for flexible operation has posed significant challenges to the control system design of solvent based post-combustion CO2 capture (PCC) process: 1) the capture system itself has very slow dynamics; 2) in the case of wide range of operation, dynamic behavior of the PCC process will change significantly at different operating points; and 3) the frequent variation of upstream flue gas flowrate will bring in strong disturbances to the capture system. For these reasons, this paper provides a comprehensive study on the dynamic characteristics of the PCC process. The system dynamics under different CO2 capture rates, re-boiler temperatures, and flue gas flow rates are analyzed and compared through step-response tests. Based on the in-depth understanding of the system behavior, a disturbance rejection predictive controller (DRPC) is proposed for the PCC process. The predictive controller can track the desired CO2 capture rate quickly and smoothly in a wide operating range while tightly maintaining the re-boiler temperature around the optimal value. Active disturbance rejection approach is used in the predictive control design to improve the control property in the presence of dynamic variations or disturbances. The measured disturbances, such as the flue gas flow rate, is considered as an additional input in the predictive model development, so that accurate model prediction and timely control adjustment can be made once the disturbance is detected. For unmeasured disturbances, including model mismatches, plant behavior variations, etc., a disturbance observer is designed to estimate the value of disturbances. The estimated signal is then used as a compensation to the predictive control signal to remove the influence of disturbances. Simulations on a monoethanolamine (MEA) based PCC system developed on gCCS demonstrates the excellent effect of the proposed controller.