As a key issue in recent international climate summits, the Green Climate Fund (GCF) is confronted with the problem of insufficient financing. This paper intends to explore several schemes for raising the public finance of the GCF among developed countries. Lessons from three main ongoing international financing mechanisms have been drawn, including the United Nations (UN) membership dues, Official Development Assistance (ODA), and the Global Environment Facility (GEF). The indexes that reflect historical emission responsibility (HR) and ability to pay (AP) are also used to share the burden. Results reveal that the ongoing international financing mechanisms vary in their burden sharing results and the shares of existing donors are driven by highly complex reasons. Weighting the HR, UN, and GEF approaches with the Preference Score Compromises (PSC) method could yield a compromise scheme in which the regional contributions are highly similar to those under the GCF initial resource mobilization from 2015 to 2018. GCF financing heavily depends on contributions from the developed countries even if the donor parties are extended to emerging economics. This paper also finds that the decision of the United States to withdraw from climate finance will significantly increase the burden for other donors, particularly for the European Union the contribution share of which is predicted to increase to nearly 14 percentage points. The schemes proposed in this study can provide a useful reference for GCF financing.