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. Boundary locus plot method is used to carry out the stability analysis of this class of methods. The methods derived herein are shown to be A-stable for step number 𝑘 ≤ 12 and are of order p=1. Numerical test on two standard linear and nonliear stiff SODEs problems in the literature are carried out. Solutions generated using the proposed class of methods show that the numerical method mimic the analytic solution. The class of method derived in this article are well suited in treatment of stiff SODEs and compete favorable with existing methods.