Abstarct: In this paper, we develop a high-order discontinuous Galerkin method for solution of Itô stochastic ordinary differential equations. we first construct an approximate deterministic ordinary differential equations with a random coefficient on each element using the well-known Wong–Zakai approximation theorem. Since the resulting ordinary differential equations converges to the solution of the corresponding Stratonovich stochastic differential equations, we apply a transformation to the drift term to obtain a deterministic ordinary differential equation which converges to the solution of the original stochastic differential equations. The corrected equation is then discretized using the standard high-order discontinuous Galerkin method for deterministic ordinary differential equations. We prove that the proposed stochastic discontinuous Galerkin method is equivalent to an implicit stochastic Runge–Kutta method. Then, we study the numerical stability of the stochastic high-order discontinuous Galerkin scheme applied to linear stochastic ordinary differential equations with an additive noise term. The method is shown to be numerically stable in the mean sense. As a result, it is suitable for solving stiff stochastic differential equations. Moreover, the method is proved to be convergent in the mean-square sense.