The simplification of simulation inevitably leads to model mismatch. In this paper, a once-through steam generator (OTSG) for a small lead bismuth fast reactor (SLBFR) is established and verified, and the OTSG model is simplified by three different methods. Based on the simplified OTSG model, IMC and IMC-PID controllers are designed to verify the sensitivity of the controller to model mismatch. The results show that the sensitivity of the controller to model mismatch is related to the filter parameters. With the increase in λ, the IMC-PID controller becomes insensitive to model mismatch caused by model linearization, non-minimum phase characteristics, noise and time delay. However, the adaptability to model mismatch sacrifices the sensitivity of the system. When λ is too large, the inertia of the controller is too large, resulting in the deterioration of the fast power regulation. Through the research of this paper, the time domain response approximation method is recommended for OTSG model simplification, and λ is recommended to be between 5 and 10 for feedwater IMC-PID controller.