The integration energy and information technology has prompted the development of the multi-carrier energy system. Energy hub model is widely used in the multi-carrier energy system study. However, it is the difficult to formulate coupling matrix and optimize operation state of complex energy hub model. This paper proposes an efficient standardized multi-step modelling method and linearized optimization method for the energy hub model. Firstly, a complex energy hub model is separated into several simple energy hub models based on nodes arrangement and virtual nodes insertion methods; then the coupling matrix of each simple energy hub model can be easily modelled; the coupling matrix of the complex energy hub model can be obtained by multiplying the coupling matrix of each simple energy hub model. In addition, energy storage, demand response and renewable energy are considered and integrated in the energy hub model. Further, the nonlinear optimal operation model of energy hub is reformulated to a linear programming problem by using variable substitution in each simple energy hub model. Cases study is performed on a resident district in a city of China on a typical summer day with the energy storage devices, demand response and renewable energy considered. Compared with the traditional calculation method, the computational burden is significantly reduced based on the proposed calculation method, which can guarantee the global optimal operation decision.