In this paper, we introduced the stochastic optimal control problem into a stochastic SVIR epidemic model with logistic growth of population and saturated incidence function with the aim to optimize the vaccination. By using the stochastic maximum principle, we analyzed the stochastic optimal control problem for this model in the case when there are no budget constraints, as well as in the case under budget constraints. We solve the optimal control problem with two types of budget constraints with a given cost constraint by using the stochastic maximum principle and generalized Lagrange multiplier method. The theoretical results for the unconstrained optimal control problem are illustrated via numerical simulations.