I explore the relationship of Environment, Social, and Governance (ESG) score on the yield spread of global corporate green bonds. Through both aggregate and segmented OLS regression analyses of the sample, I examined the impact of ESG scores on the overall sample and compared the differential effects on green bonds and conventional bonds based on the cross-sectional data. Additionally, I provided evidence of the impact of ESG scores on corporate bond yield spreads across various industries. I find that there is a negative relationship between ESG score and corporate bond yield spreads generally while G-Score contributes most to the relationship, but green bonds have a yield spread premium over conventional bonds at the special given day. In heterogeneity analysis, results show that (i) ESG score has a positive relationship with green bonds yield spread; (ii) Green bonds in the bank and electric utilities industry exhibit a significant higher yield spread. (iii) ESG score has a significant negative relationship with Eurobonds yield spread while it has a significant positive relationship with US corporate bonds yield spreads. (iv) Bonds issued by the A, B, and C-graded firms had significantly lower bond yields (higher bond prices) than the lowest ESG D-grade. The findings are broadly coherent with the argument in the existing literature that ESG score has a negative relationship with corporate bond yield. However, the positive relationship between ESG scores and green bond yield spreads observed in the results indicates that the "greenium" is diminishing now, guiding us towards further research on greenwashing and bond pricing mechanisms.