Non-intrusive load monitoring, a convenient way to discern the energy consumption of a house, has been studied extensively. However, most research works have been carried out based on a hypothetical condition that each electric appliance has only one running state. This leads to low identification accuracy for multi-state electric appliances. To deal with this problem, a method for identifying the type and state of electric appliances based on a power time series is proposed in this paper. First, to identify the type of appliance, a convolutional neural network model was constructed that incorporated residual modules. Then, a k-means clustering algorithm was applied to calculate the number of states of the appliance. Finally, in order to identify the states of the appliances, different k-means clustering models were established for different multi-state electric appliances. Experimental results show effectiveness of the proposed method in identifying both the type and the running state of electric appliances.