Abstract Global exponential stability problem of impulsive inertial neural networks with time-varying discrete-delay and distributed-delay is considered in the present paper. Lyapunov–Krasovskii functional and differential inequality for delay differential equations are employed to investigate the stability of the inertial neural networks. The distributed-delay-dependent stability criteria are obtained in terms of linear matrix inequalities and algebraic inequalities. The novel results complement and extend the works on inertial neural network with/without impulsive effects. Finally, typical numerical examples are given to illustrate the validity of the theoretical results.