In this paper, the stability analysis problem is investigated for delayed neural networks with mixed time-varying delays, impulsive control and Markovian jumping parameters. The mixed time-varying delays include leakage, discrete and distributed time-varying delays. Sufficient conditions for the global exponential stability in the mean square are derived by using Lyapunov–Krasovskii functional having triple integral terms and model transformation technique. The stability criterion that depends on the upper bounds of the leakage time-varying delay and its derivative is given in terms of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical softwares. Finally, three numerical examples and simulations are given to demonstrate the usefulness and effectiveness of the presented results.