This paper discusses the stability for stochastic singular systems with state-dependent noise in both continuous-time and discrete-time cases. Firstly, the condition for the existence and uniqueness of the solution to stochastic singular systems is given. Based on this condition, the stochastic Ito singular system is transformed into a deterministic standard singular system by means of H-representation method. Secondly, new sufficient conditions for the stability of systems considered are derived in terms of strict linear matrix inequalities. Finally, an example is given to illustrate the effectiveness of the obtained theoretical results. (C) 2014 Elsevier Ltd. All rights reserved.