We investigate the state feedback stabilization, in the sense of weak solution, of nonlinear stochastic systems when the drift is quadratic in the control and the diffusion term is affine in the control. Based on the generalised stochastic Lyapunov theorem, we derive the necessary conditions and the sufficient conditions, respectively, for the global asymptotic stabilization in probability by a continuous feedback explicitly computed. The interest of this work is that the existing control methods are inapplicable to a lot of systems contained in the class of stochastic systems considered in this paper.