Non-intrusive load monitoring (NILM) aims to decompose aggregated electrical usage signal into appliance-specific power consumption and it amounts to a classical example of blind source separation tasks. Leveraging recent progress on deep learning techniques, we design a new neural NILM model Multi-State Dual CNN (MSDC). Different from previous models, MSDC explicitly extracts information about the appliance's multiple states and state transitions, which in turn regulates the prediction of signals for appliances. More specifically, we employ a dual-CNN architecture: one CNN for outputting state distributions and the other for predicting the power of each state. A new technique is invented that utilizes conditional random fields (CRF) to capture state transitions. Experiments on two real-world datasets REDD and UK-DALE demonstrate that our model significantly outperform state-of-the-art models while having good generalization capacity, achieving 6%-10% MAE gain and 33%-51% SAE gain to unseen appliances.