Stochastic Ordinary Differential Equations (SODEs) are often insoluble via the use of analytic techniques due to randomness that characterize SODEs. Stiffness in SODEs introduces complexity in that numerical method for approximating the solution of stiff SODEs are required to be A-stable, a stringent condition that is attainable by implicit method only. This article presents a class of A-stable methods, that derived via the use of Ito Taylor expansion, Taylor series expansion and method of undetermined coefficients.