A substantial investment gap exists in financing climate change adaptation in emerging markets. Governments could mobilize private capital through the green bond market to help close the gap. However, the relative cost of adaptation capital facing emerging markets remains unclear. To understand this, we analyze the green premium (Greenium) of 444 green bonds issued by governments and public agencies across 35 countries globally, spanning 17 currencies. Our results indicate that, among green bonds from emerging markets, the Greenium of adaptation bonds (green bonds whose use of proceeds includes climate change adaptation) is larger than that of non-adaptation bonds. The former is even larger if these adaptation bonds are from countries with higher physical risk exposure or stronger governance capacity. Notably, even among countries with above-median physical risk exposure, the Greenium of adaptation bonds from emerging markets is still larger than that from developed markets. Our results show the potential for emerging markets to mobilize more private capital in the green bond market to supplement public finance in supporting climate change adaptation.