AbstractThis article extends stochastic input‐to‐state stability () to stochastic time‐delayed hybrid systems with the properties of edge dependent. By quoting multiple Lyapunov–Krasovskii functional, comparison principle in association with admissible edge‐dependent average dwell time () approach and admissible amputated edge‐dependent average impulsive interval () technology, several novel stability criteria of hybrid time‐delayed stochastic systems are established. We allow impulsive jump and subsystem switching to occur at different instants. Furthermore, a new method named AAED‐AII is recommended for gap between impulses, which is an improvement for mode‐dependent average impulsive interval. Finally, a practical example is given to show the effectiveness of the new design techniques.