<p>The paper is devoted to the construction and analysis of stochastic gradient methods based on explicit Runge–Kutta schemes. We propose second-order differential equations for the dynamics of the gradient method with a variable stepsize in deterministic and stochastic cases. The theorem on the convergence rate of trajectories to the stationary point is formulated. For the construction of gradient methods the assumption on approximation of stochastic term is used. It provides the possibility to avoid the use of stochastic Runge–Kutta methods and to construct methods based on well-developed schemes for deterministic case. In contrast with methods with adaptive stepsize, the proposed method simply uses the available gradient information without modifications. The constant stepsize of the Runge–Kutta scheme is used and it provides the possibility to make each step to be longer for the schemes with good stability properties. Sufficient conditions on stepsize and parameters, which guarantee convergence on expectation, are obtained. As it is demonstrated, the convergence rate is dependent on the parameters of stepsize diminishing law and the smoothness of the objective function and is independent of the accuracy order and parameters of the Runge–Kutta method. By the proper tuning of the parameters, the rate can be done close to the rates of well-known stochastic gradient methods. The effectiveness of the proposed method in the case of a second-order explicit scheme with two stages in comparison with the stochastic gradient descent method, Nesterov’s accelerated method, and Adam optimizer is demonstrated in different numerical experiments on convex and non-convex functions. As it is obtained, the new method required less number of iterations and computational time in comparison with well-known methods.</p>