Aiming at the problem of wind curtailment caused by the lack of system flexibility, an optimal scheduling strategy for improving the flexibility of the electricity-gas-heat interconnection system by the coordinated operation of the gas network management and storage characteristics and the heat storage characteristics of the heat network is proposed. Firstly, the influence of gas network storage and heat network storage on improving flexibility is analyzed respectively. Then, an electricity-gas-heat interconnected system scheduling model considering the dynamic characteristics of gas network management and t the delay characteristics of heat storage in heat network, which greatly improves the imbalance between supply and demand of flexibility in space and time brought by the anti-peak regulation characteristics of wind power to the system. Finally, the IEEE-24 nodes power system, Belgium’s 20-node natural gas network and 6-node thermal network are used, for example, analysis. The results show that the proposed scheduling scheme improves the flexibility of the system while its operating cost and wind curtailment cost are the lowest, which promotes the consumption of wind power.