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In this paper, we construct a stochastic SVEAIR (Susceptible-Vaccinated-Exposed -Asymptomatic-Infected-Removed) epidemic model. It aimed to investigate COVID-19 control strategies through four different control methods, which consist of prophylaxis, vaccination control, rapid screening of people in exposure categories, and people identified as infected without screening. Firstly, we study the optimal control model and obtain the optimal control strategy using stochastic control theory. Secondly, the optimal control model with control term or without control term is numerically analyzed by using the implicit Runge-Kutta approximation method. At last, The numerical simulations verify the theoretical results and it show that control could help reduce infection and improve population health.