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Currently, the significance of social media in disseminating noteworthy information on topics such as health, politics, and the economy is indisputable. During the COVID-19 pandemic, anti-vaxxers have used social media to distribute fake news and anxiety-provoking information about the vaccine. Such social media practice may harm the public. Here, we characterise the psycho-linguistic features of anti-vaxxers on the online social network Twitter. For this, we collected COVID-19 related tweets from February 2020 to June 2021 to analyse vaccination stance, linguistic features, and social network characteristics. Our results demonstrated that, compared to pro-vaxxers, anti-vaxxers tend to have more negative emotions, narrative thinking, and immoral tendencies. Furthermore, we found a tighter network structure in anti-vaxxers even after mass vaccination. This study can advance our understanding of the online anti-vaccination movement, and become critical for social media management and policy action during and after the pandemic.