We present Adapt, a new white-box testing technique for deep neural networks. As deep neural networks are increasingly used in safety-first applications, testing their behavior systematically has become a critical problem. Accordingly, various testing techniques for deep neural networks have been proposed in recent years. However, neural network testing is still at an early stage and existing techniques are not yet sufficiently effective. In this paper, we aim to advance this field, in particular white-box testing approaches for neural networks, by identifying and addressing a key limitation of existing state-of-the-arts. We observe that the so-called neuron-selection strategy is a critical component of white-box testing and propose a new technique that effectively employs the strategy by continuously adapting it to the ongoing testing process. Experiments with real-world network models and datasets show that Adapt is remarkably more effective than existing testing techniques in terms of coverage and adversarial inputs found.