This paper examines the dynamic conditional correlations among 10 cryptocurrencies and the possibility of hedging investment strategies among multiple cryptocurrencies over the period affected by COVID-19 from 2017 to 2022. After studying the relationship between Bitcoin, Ethereum, and the other eight cryptocurrencies, four main results were obtained in this paper: first, from the pre-COVID-19 period to the COVID-19 period, almost all of the cryptocurrencies’ return growth rates increased, and COVID-19 had a positive effect on the returns of cryptocurrencies. Second, all of the cryptocurrencies’ return indices had features of volatility clustering and memory persistence in the long run; from pre-COVID-19 to COVID-19, these cryptocurrencies’ GARCH values decreased, but the correlations among the varying GARCH values increased. Third, the varying correlations between the return indices of Bitcoin, Ethereum, and the other cryptocurrencies were very strong; from pre-COVID-19 to COVID-19, the average dynamic correlations between Bitcoin and the others increased. Fourth, Tether can be used as a hedge cryptocurrency against the other cryptocurrencies as COVID-19 enhanced its hedging feature.