After the vaccine implementation for COVID-19, the WHO set a unified vaccination approach to be adopted by all different countries. However, given the various constraints including vaccine availability, heterogeneous age distributions, and differing control measures across countries, questions arise about the optimality of the WHO strategy. In this study, we develop an age-structured SEIR epidemic model with vaccinated and unvaccinated compartments to optimize age-targeted vaccination strategies for COVID-19, incorporating realistic constraints. The model equilibria and the basic reproduction number $R_0$ are checked. Moreover, mathematical formulation and analysis of optimal control problem, are conducted. The model is calibrated to COVID-19 data and simulated to solve the optimal control problem under various vaccination and distancing scenarios. Results demonstrate that the optimal strategy strongly depends on the population age distribution and contact patterns.  Findings emphasize the significance of age-specific disease transmission in designing vaccination priorities, particularly when vaccine supplies are constrained. The model provides a quantitative framework to inform optimal allocation strategies in a general way that allows to adapt the model for other infectious diseases exhibiting similar features to Covid-19.