In order to solve the frequently occurred nonlinear working characteristics problem of the devices in integrated energy system (IES), where this nonlinear problem causes the offset of operation characteristics and design points of those devices, in this paper, the hierarchical multi-objective fuzzy collaborative optimization model of IES under off-design performance is proposed. Firstly, the high-order nonlinear models of devices under off-design performance, including fuel cell (FC), gas turbine (GT), absorption lithium bromide chiller (ABS), etc., are presented considering renewable energy and diversified storage devices, which can more accurately describe the actual working condition of devices. Secondly, according to the needs of different engineering application modes, the lower level collaborative optimization model of energy hub (EH) with economic, eco-friendly, primary energy saving, and renewable energy accommodation rate as optimization objectives is proposed, which can well adapt to and reflect real world energy system. Thirdly, based on the relationship between master and slave dispatch centers, the upper level modeling and optimal scheduling model of IES consisting of coupling power system, natural gas system, and heat system is proposed. Then, a multi-objective fuzzy collaborative optimization model for EH and IES is developed, where continuous differentiable Sigmoid function is taken as the membership function. Finally, simulation results show that the proposed models and optimal dispatch method can effectively solve the frequently occurred non-linear working characteristics problem of the devices in IES. The optimal results are suitable for planning, calculation, operation, dispatch of IES, which can reasonably reflect the operation characteristics of IES.