The green bond market has gradually developed worldwide since its debut in 2007 and is viewed as a new form of investment. This study explores the time-varying interdependence between green bond and conventional asset classes, namely Bitcoin price, Standard and Poor’s (S&P) 500, Clean Energy Index, Goldman Sachs Commodity Index (GSCI) Commodity Index and 10-year US bond spanning from May 2013 to December 2019, using both time-varying copula and transfer entropy models. We first focus on static and dynamic correlations between the green bond and other assets, and then identify the causal association among them. The findings suggest that green bonds and other assets have conditional time-varying dependence, and dependence is relatively low. Using transfer entropy, further evidence is gained for causal associations between two variables, which is depicted by two categories like mono-direction and bi-direction. Such nexus reveals the transmitter and receiver of return innovations on these markets. These findings make a considerable contribution to policymakers and environmentally friendly investors with green bond positions.