A suboptimal approach to attack stochastic control problems, when the well known Linear-Quadratic-Gaussian (LQG) algorithm cannot be used, is proposed in this paper. The stochastic system here considered is described by an observable Ito equation with linear drift and bilinear diffusion. The aim of this paper is to provide the suboptimal linear feedback (SLF) control law, with optimality criterion given by the classical quadratic cost function, for this class of nonlinear systems. The SLF control is indeed an appropriate setting that guarantees a tradeoff between easy implementation and meaningful control-goal, whereas in general the optimal control problem involves the integration of an infinite-dimensional system.