This article investigates <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> synchronization of delayed neural networks under a receding horizon scheme, where two types of interval time-varying delays are considered according to whether the lower bound of the delay derivative is known or not. Note that a receding horizon synchronization law can be regarded as an optimization solution at each timeslot to a minimaxization problem related closely with a certain cost functional. In this article, two cost functionals with some delay-dependent matrices are introduced, respectively, for the two types of time delays. In order to obtain less conservative conditions, a novel inequality on quadratic polynomial functions is established, which includes some existing ones as its special cases. Based on the novel inequality, two sufficient conditions are derived to design the terminal weighting matrices of the cost functionals such that the resulting synchronization error system can be stabilized with a prescribed infinite horizon <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance level. Finally, three numerical examples are used to demonstrate the validity of the proposed results.