In this paper we study the numerical treatment of Stochastic Differential Equations with additive noise and one dimensional Wiener process. We develop two, three and four stage Runge–Kutta methods which attain deterministic order up to four and stochastic order up to one and a half specially constructed for this class of problems. Numerical tests and comparisons with other known methods in the solution of various problems justify our effort, especially for our three stages methods.