There is a growing tendency to replace coal heating with electric heating in urban heat supply systems to reduce the air pollution and achieve defossilisation. To promote the use of electric heating, the economic incentive from governments will play a decisive role. This paper investigates the impact of taxation and subsidy policies on the long-term evolution of urban heat supply systems based on the evolutionary game theory. The evolutionary stable strategy is calculated which yields the fraction of each kind of heating strategy as well as the regulatory policy in a steady state. Four scenarios including both static and dynamic policy design mechanisms are simulated. The dynamic policy design is formulated as an optimal control problem, and the optimal evolutionary trajectory is obtained from the proposed optimal parameter design algorithm. Simulation results indicate that the amount of electric heating can be flexibly and accurately controlled by the government through the design of taxation and subsidy policies. It is shown in the case study that taxations could be more efficient than subsidies to encourage using electric heating, and a combination of dynamic taxation and dynamic subsidy policies can expedite the heating system electrification process. (C) 2019 Elsevier Ltd. All rights reserved.