The stark contrast between different opinions on COVID-19 vaccination suggests that the underlying opinion dynamics is a topic worth studying. Here we build a comprehensive agent-based model by incorporating fear into the HUMAT framework to study how the availability heuristic and confirmation bias influence information processing and impact the opinion dynamics and vaccination rate in the case of the COVID-19 pandemic. Three scenarios are designed to explore the impact of the disease severity, confirmation bias, and authorities on COVID-vaccination opinion polarisation and the vaccination rate. Main simulation results indicate that: 1) Increased fear of disease raises the vaccination rate and accelerates people’s uptake of COVID vaccines. 2) Confirmation bias fuels opinion polarisation through the mechanism of information selection and improves the satisfaction of different groups. 3) Opposing authorities and availability heuristic promote opinion polarisation, while more moderate authorities reduce polarisation but do not make it disappear. Implications of these results are discussed for science communication related to complex societal problems.