In this paper, we propose an age-structured epidemic model with strain mutation and age-based vaccination. We define the reproduction numbers of both the original and mutant strains ($R^1_0$ and $R^2_0).$ If the reproduction number $R_0 < 1,$ the disease-free steady state is locally asymptotically stable. If the reproduction number $R^2_0 >1,$ there exists a dominant steady state of the mutant strain. Conditions for local stability of this dominant steady state are also obtained. If both reproduction numbers $R^1_0$ and $R^2_0$ are greater than 1, a coexistence steady state may occur. Finally, the uniform persistence of the disease described by our age structured model is strictly proved when the reproduction number $R^1_0 > 1.$ By using the data of the COVID-19 epidemic in Wuhan and the theoretical results obtained in this paper, some numerical calculations are carried out to prove the effect of the age-based vaccination strategy.