This paper is concerned with numerical techniques of solving a class of stochastic optimal control problem with the performance criterion taken as the probability of hitting a target. The system under consideration is governed by an I to stochastic differential equation. Such problems have been considered by Katayama and also by Van Mellaert and Dorato. However, they assumed that the controluappears linearly in the system equations. In addition, Katayama only computed time-invariant controls, while Van Mellaert and Dorato investigated a special case where the control directly affects only one component of the state variable. This paper presents a technique that works even if the control appears non-linearly in the system equations.