In this paper, the stability of a type of neural network with time-varying delay is studied. Two general (α,β) and (α,β,γ)-dependent reciprocally convex inequalities with two and three terms are derived to introduce some quadratic terms into the estimate for the derivative of the Lyapunov–Krasovskii functionals (LKFs). The LKF method is used to develop a stability criterion for time-delay neural networks by using the new inequalities. To demonstrate the improvement of the new criterion, numerical results are provided.