We study the stability properties of switched stochastic neural networks (SSNNs) with time-varying delays whose subsystem is not necessarily stable. We introduce state-dependent switching (SDS) as a tool for stability analysis. Some SDS laws for asymptotic stability and p th moment exponentially stable are designed by employing Lyapunov-Krasovskii (L-K) functional and Lyapunov-Razumikhin (L-R) method, respectively. It is shown that the stability of SSNNs with time-varying delays composed of unstable subsystems can be achieved by using SDS law. The control gains in the designed SDS laws can be derived by solving the LMIs in derived stability criteria. Two numerical examples are provided to demonstrate the effectiveness of the proposed SDS laws.