The design margin is defined as the value added on the nominal value of a design variable, which must be determined not only for process uncertainties but also for dynamic control, but its size cannot be too large in consideration of device and operation costs. In the fluid catalytic cracking unit (FCCU), the catalyst inventory and the air flow rate of regenerator are important design variables, so it is necessary to analyze the relationship between their margins and control performance. In this paper, the design margins of catalyst inventory and air flow rate under model predictive control are solved via dynamic optimization. A linear model predictive control is used based on the linear state space model obtained by linearization of the steady-state nominal operating point. The relationship between the control performance and the design margin is discovered by changing the prediction horizon. It can be found that improving the control performance requires more air flow rate margin but less catalyst inventory margin for the process. An inflection point on the relationship curve exists between control performance and air flow rate margin. The prediction horizon of the model predictive control should be determined based on the inflection point to improve the process control performance significantly with a lower air flow rate margin cost.