We develop a susceptible--vaccinated--infected--waned--recovered--deceased (SVIWRD) epidemic model with a continuous age structure to capture age-dependent heterogeneity in vaccination outcomes and disease transmission. Compared with population-level or coarsely age-grouped models, the age-discretized framework provides a more refined description of age-specific infection risk, vaccine protection, natural mortality, and disease-induced mortality. A saturated nonlinear force of infection is incorporated to reflect the upper bound of infectiousness when the number of infectious individuals becomes large. Using Pontryagin`s maximum principle, we derive the fully coupled adjoint system and characterize the optimal age-dependent vaccination strategy. For numerical implementation, the age-structured partial differential equation system is discretized into an ordinary differential equation system, and the optimal control is computed by a forward--backward sweep algorithm. Numerical results show that the optimal age-dependent vaccination policy reduces both infections and deaths compared with a uniform allocation strategy, with a clear age-specific prioritization pattern. This study provides a mathematical framework for designing targeted vaccination strategies under limited vaccine resources.