Support for renewable energy currently is revised in many countries due to the perception that the economic burden caused by the support exceeds the permissible limit. Decreased or suspended support creates instability in renewable energy production. There is a lack of research related to design of the sustainable renewable energy support policy, which considers the structure of the support policy system in detail leading to successful implementation of such support. The aim of the study was to create the model which helps to devise biomethane supply support policy providing controllable and stable growth of biomethane production over time avoiding relapsed “overshoots and oscillations” in the system. Due to the dynamic and complex character of energy supply system policy decisions, system dynamics was used as the method. The results show that the main parameters which have an impact on stability of the support policy are feedbacks linking the total biomethane support payments, the granted permits, the perceived limit of the support, willingness to invest in the production assets as well as time delays of the action resulting from the feedbacks. The results show that biomethane production can reach up to 610 GWh with the support of 66 EUR per MWh in 2030 without exceeding the perceived support limit and avoiding fluctuations in the system. The developed method-model can be used by the researchers and energy policy developers to study the dynamics of investments into biomethane supply systems and the resulting biomethane production volumes depending both on the sizes of the subsidies provided for the biomethane as well as the structure of the support system.