The accuracy of the simulation model has a profound impact on the optimal operation of the energy hubs (EHs). However, in many articles, the constant model of the efficiency of equipment is adopted to formulate the operation system, which would probably lead to a simplification of the simulation models. But, EHs are typically operated under off-design condition due to the fluctuations in cooling, heating, electricity requirement. Moreover, even though the off-design characteristics are considered, few studies have suggested comparing the differences between those two models by considering the operation cost. In order to assess the effect of the off-design characteristics of EH on the optimal operation accuracy in this paper, two test cases are performed on the fixed and variable load conditions, respectively. In addition, the individual effect of off-design characteristics of each equipment on the optimal operation cost of the EH is also investigated through four optimization runs. It is worth mentioning that the optimal operation problem of the EH considering the off-design characteristics and on-off status of the equipment is a mixed integer non-linear programming problem (MINLP). By testing the design and off-design models on the two cases, the results of simulation demonstrate that the optimal operation cost for the off-design model is larger than that for the design model. Nonetheless, in the aspect of the authenticity of the system operation strategy, the off-design model performs better than the design model. Furthermore, a larger relative error of the system operation cost between the two models can be observed when the EH is operated under a relatively lower load condition, revealing that the influence of off-design characteristic on the optimal operation of EHs is too significant to be neglected.