Working memory refers to the brain's ability to store and manipulate information for a short period. It is disputably considered to rely on two mechanisms: sustained neuronal firing, and “activity-silent” working memory. To develop a highly biologically plausible neuromorphic computing system, it is anticipated to physically realize working memory that corresponds to both of these mechanisms. In this study, we propose a memristor-based neural network to realize the sustained neural firing and activity-silent working memory, which are reflected as dual functional states within memory. Memristor-based synapses and two types of artificial neurons are designed for the Winner-Takes-All learning rule. During the cognitive task, state transformation between the “focused” state and the “unfocused” state of working memory is demonstrated. This work paves the way for further emulating the complex working memory functions with distinct neural activities in our brains.