The risk for severe illness and mortality from COVID-19 significantly increases with age. As a result, age-stratified modeling for COVID-19 dynamics is the key to study how to reduce hospitalizations and mortality from COVID-19. By taking advantage of network theory, we develop an age-stratified epidemic model for COVID-19 in complex contact networks. Specifically, we present an extension of standard SEIR (susceptible-exposed-infectious-removed) compartmental model, called age-stratified SEAHIR (susceptible-exposedasymptomatic-hospitalized-infectious-removed) model, to capture the spread of COVID-19 over multitype random networks with general degree distributions. We derive several key epidemiological metrics and then propose an age-stratified vaccination strategy to decrease the mortality and hospitalizations. Through extensive study, we discover that the outcome of vaccination prioritization depends on the reproduction number R0. Specifically, the elderly should be prioritized only when R0 is relatively high. If ongoing intervention policies, such as universal masking, could suppress R0 at a relatively low level, prioritizing the high-transmission age group (i.e., adults aged 20-39) is most effective to reduce both mortality and hospitalizations. These conclusions provide useful recommendations for age-based vaccination prioritization for COVID-19.