Recently, people have been being vaccinated the vaccine against covid-19 for some time, but the vaccine is new, while people want to obtain immunity through vaccination, they are also worried about the efficacy and side effects after vaccination. Not everyone is absolutely willing to get vaccinated. A typical idea resistant to vaccination is that if the people around the individual itself are vaccinated, the individual itself will not be infected without being vaccinated and will not have to bear the risk of vaccination. We call this neighbor-reliant immunity(NRI). In this article, we mainly studies how the trust in vaccines against COVID-19 and the reliance on neighbors affect individuals' attitude toward vaccination and the process of vaccination based on network. Every time how the willingness to get vaccinated of the individual itself changes is affected by the vaccination performance of its neighbors. What we can find is that when people's trust in vaccines increases or their reliance on neighbors increases, it will lead to an increase in the rate of vaccination and speed up the process of vaccination.