The anti-vaccine movement has been gaining traction in many countries since the COVID-19 pandemic began. However, their aggressive behaviour in replies—the form of directed messaging that can be sent beyond follow-follower relationships—is still less understood, and even less so about their differences in languages. We conducted a comparative study of anti-vaxxers’ aggressive behaviours by analysing a longitudinal dataset of COVID-19 tweets in English and Japanese. We found two common features across these languages. First, anti-vaxxers most actively transmit targeted messages or replies to users with different beliefs, especially to neutral accounts, with significantly toxic and negative languages; these replies are often directed to posts about vaccine operations. Second, the influential users with many followers and/or with titles are more likely to receive the most toxic replies from the anti-vaxxers. However, pro-vaccine accounts with a few followers even receive highly toxic replies in English, which calls for a special aid different from the Japanese case. These results provide insights into both language dependent and independent countermeasures against anti-vaxxers’ aggressive behaviour.