A non-intrusive load monitoring method based on Gaussian mixture model clustering combined with a deep neural network is proposed to explore the potential of energy saving and emission reduction at the customer side. It also fine-tunes the analysis and management of customer electricity consumption behavior, and improves the efficiency of electricity use. First, we tackle the problem that the same electrical appliance often has similar power but inconsistent operating status. In order to classify the load working status in fine manner, the advantages of "soft classification" and flexible clustering in the Gaussian mixture model clustering algorithm can be used to form a load status feature library that conforms to the actual operating conditions of electrical equipment. Secondly, note that in the common deep neural networks applied to non-invasive load monitoring models, there are problems such as low recognition accuracy in multi-label classification. Thus a deep neural network model with a mixture of convolutional neural networks and gated recurrent units is proposed. Finally, the validation analysis is carried out on the AMPds2 dataset by considering the influence of external environmental data on the energy consumption habits of household users, and the results are compared with other models. The results show that the proposed non-invasive load monitoring model has high accuracy. This work is supported by the National Natural Science Foundation of China (No. 61872230).