This work considers the problem of mean-square stochastic stability analysis of hybrid stochastic inertial neural networks (INNs) with the effect of time-delays. Here, the hybrid stochastic INNs are represented as the combination of a two-level system in which the first level is directed by the system of second-order differential equations and the second level is directed by the discrete set representing the switch (jump) nodes. Initially, sufficient delay-dependent mean-square stability conditions for the hybrid INNs with time-delays are established using variable transformation techniques and some integral inequalities. This process is carried out mainly based on Lyapunov theory and linear matrix inequality technique. Some general cases on time-delay such as time-varying delay, interval time-varying delay, and mode-dependent delay are considered and corresponding results are established. Finally, numerical examples pertaining to the validation and effectiveness of the derived theoretical results are demonstrated. © 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.