In this paper, the problem of robust stability analysis for a type of uncertain stochastic switched inertial neural networks (SSINNs) with time-varying delay is investigated. First, the original second-order system is converted into first-order differential equations using the variable transformation method. Next, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained using Lyapunov-Krasovskii functional (LKF), state-dependent switching (SDS) method, and Jensen's integral inequality for estimating integral inequalities so that the augmented system is robust, global, and asymptotically stable in the mean square for the uncertain SSINNs with time-varying delay. It is shown that the stability of the above considered system composed of all unstable subsystems can be achieved by using the SDS law. Finally, two numerical simulations are provided to demonstrate the effectiveness of the proposed SDS law.