We examined co-movement between green bonds and triple-A government bonds during December 2008-“November 2019. We determined that two markets followed the heavy tail dependence using Student’s t-copulas. Using transfer entropy, further evidence was obtained for the causal relationship between the two markets, which was described by three categories such as -no effect, -mono-direction,’ and -bi-direction’; this relationship indicated the sender and the receiver of return shocks on these markets. Our results highlight the presence of contagion risk between green bonds and prime government bonds, which has practical implications for risk management.