Non-intrusive load monitoring (NILM) is a well-known single-channel blind source separation problem that aims to decompose the household energy consumption into itemised energy usage of individual appliances. In this way, considerable energy savings could be achieved by enhancing household's awareness of energy usage. Recent investigations have shown that deep neural networks (DNNs) based approaches are promising for the NILM task. Nevertheless, they normally ignore the inherent properties of appliance operations in the network design, potentially leading to implausible results. We are thus motivated to develop the dual Deep Neural Networks (dual-DNN), which aims to i) take advantage of DNNs' learning capability of latent features and ii) empower the DNN architecture with identification ability of universal properties. Specifically in the design of dual-DNN, we adopt one subnetwork to measure power ratings of different appliances' operation states, and the other subnetwork to identify the running states of target appliances. The final result is then obtained by multiplying these two network outputs and meanwhile considering the multi-state property of household appliances. To enforce the sparsity property in appliance's state operating, we employ median filtering and hard gating mechanisms to the subnetwork for state identification. Compared with the state-of-the-art NILM methods, our dual-DNN approach demonstrates a 21.67% performance improvement in average on two public benchmark datasets.