This study contributes to the debate on safe-haven characteristics of environmental, social, and governance (ESG) stocks during COVID-19 pandemic. Using wavelet coherence framework on four major ESG stock indices from global and emerging stock markets, and two proxies of COVID-19 fear over the period from February 5th, 2020, to March 18th, 2021, we find a strong and positive co-movement between health fear index of COVID-19 and returns on ESG stocks suggesting the existence of safe-haven properties in ESG stocks. However, we also observe a negative co-movement between stock market base proxy of COVID-19 and returns on ESG indices, suggesting that safe-haven properties of ESG stocks are contingent upon the proxy of COVID-19 pandemic. Our findings are of particular interest for the investors and asset managers who may use ESG stocks to diversify their portfolios during health crisis due to COVID-19 pandemic.