In this work, we obtain strong-order conditions of the Runge-Kutta method for the optimal control of the stochastic differential equations. We follow the discretize then optimize approach in order to get the optimality system. We compare Stratonovich-Taylor expansions of the exact solution and approximation method of the stochastic optimal control problem defined by the Runge-Kutta scheme successively to get the strong-order conditions. We derive the strong order-1.5 conditions and verify by a numerical example. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.