This paper studies the stability criterion of integral time-varying recurrent neural networks (RNNs) with zero lower bound and finite-time synchronization based on improved sliding mode control (SMC). Firstly, a sufficient criterion for universal asymptotic stability of RNNs with integral time-varying delays is obtained by estimating a tight upper bound of augmented Lyapunov-Krasovskii functional (LKF) derivative with inequality scaling technique and mutually convex combined inequality. Secondly, in order to eliminate the time that error system state trajectory slides along sliding mode flow pattern until convergence at the origin, based on drive response and SMC theory, a suitable sliding mode controller is designed by considering that sliding mode flow pattern is equal to synchronization error. Finally, maximum allowable upper bound of delay under different delay derivatives are obtained by considering trajectory change of input function under different initial value. Synchronization trajectory of drive and response systems with mismatched parameters and activation functions under the influence of controller are studied, and synchronization time which is required for error system to reach stability is obtained. Simulation results show that the introduction of integral delay can be more comprehensive from both difference and area, so that drive system state is eventually steady at equilibrium point and synchronized with response system. Stability criterion of this paper not only has less conservative and computation complexity but also has shorter synchronization control time.