This paper focuses on black-start of power system with turbine based combined cooling, heating and power (CCHP) systems as start units. Firstly, the relation among inrush current, the capacity of CCHP systems and transformers are researched and summarized by building models and running simulations in PSCAD. Then three typical black-start cases are designed based on the distribution network, and simulation models of the cases are built. Finally, simulations of the cases are run and the results of them are analyzed. It is affirmative that the simulation findings will be significantly valued for the planning of black-start and the design of CCHP systems.