This article analyzes the exponentially stable problem of neural networks (NNs) with two additive time-varying delay components. Disparate from the previous solutions on this similar model, switching ideas, that divide the time-varying delay intervals and treat the small intervals as switching signals, are introduced to transfer the studied problem into a switching problem. Besides, delay-dependent switching adjustment indicators are proposed to construct a novel set of augmented multiple Lyapunov-Krasovskii functionals (LKFs) that not only satisfy the switching condition but also make the suitable delay-dependent integral items be in the each corresponding LKF based on each switching mode. Combined with some switching techniques, some less conservativeness stability criteria with different numbers of switching modes are obtained. In the end, two simulation examples are performed to demonstrate the effectiveness and efficiency of the presented methods comparing other available ones.