In order to improve the balance of energy supply and demand and reduce energy consumption, the design of digital twin system of energy Internet under the background of "double carbon" is proposed. The physical perception layer, transmission interaction layer, data sharing layer, application service layer, virtual space and security protection constitute the overall framework of the digital twin system of energy Internet. Starting from the two objectives of carbon dioxide emissions and capacity investment cost, the objective function is constructed. Based on relevant constraints, the harmonic search algorithm is applied to solve the objective function, so as to realize the planning of the energy Internet and complete the design of the digital twin system of the energy Internet. The experimental results show that the gas consumption, water consumption and electricity consumption of the designed system are low, and the storage battery capacity is high, and the energy supply and demand are balanced.