Although as an advanced energy utilization approach, the performance of combined cooling, heating, and power (CCHP) system is susceptible to its configuration and operation strategy. Energy price will also affect the system performance indirectly by influencing the system's design scheme. In this paper, a linear programming (LP) based optimization model is formulated to obtain the optimal design scheme that minimizes the annual total cost of typical CCHP systems, and a comprehensive assessment framework involving economic, energy, exergy, and ecological (4E) aspects is established to assess the system performance roundly. Taking a CCHP project in Xian, China as the specific case, the design and assessment of the CCHP system are completed and sensitivity analyses for two steps, namely configuration design step and operation strategy design step, are carried out to explore the impacts of energy price fluctuation on the design scheme and performance of the system. In this process, the coupling relationship between the purchase price of natural gas and electricity are considered, and as a special form of energy price, the effects of the feed-in tariff are also discussed. The results show that the performance of the CCHP system is superior to the separate generation (SG) system in 4E aspects, reducing the running and maintenance cost, primary energy consumption, and greenhouse gas emissions by 18.63%, 24.77%, and 31.88%, respectively, and promoting the exergy efficiency by 30.87%. The feed-in tariff lower than or equal to the electricity price will have positive effects on the overall performance of the CCHP system, and a lower natural gas price and a higher electricity price are benefit for playing the advantages of the system.