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Residential demand response is vital for the efficiency of power system. It has attracted much attention from both academic and industry in recent years. Accurate short-term load forecasting is a fundamental task for demand response. While short-term forecasting for aggregated load data has been extensively studied, load forecasting for individual residential users is still challenging due to the dynamic and stochastic characteristic of single users' electricity consumption behaviors, i.e., the variability of the residential activities. To address this challenge, this paper presents a short-term residential load forecasting framework, which makes use of the spatio-temporal correlation existing in appliances' load data through deep learning. Multiple time series are conducted in the framework to describe electricity consumption behaviors and their internal spatio-temporal relationship. And a method based on deep neural network and iterative ResBlock is proposed to learn the correlation among different electricity consumption behaviors for short-term load forecasting. Experiments based on real world measurements have been conducted to evaluate the performance of the proposed forecasting approach. The results show that both the appliances' load data and iterative ResBlocks can help to improve the forecasting performance. Compared with existing methods, measurements on Root Mean Squared Error, Mean Absolute Error and Mean Absolute Percentage Error for the proposed approach are reduced by 3.89%-20.00%, 2.18%-22.58% and 0.69%-32.78%. In addition, further experiments are conducted to evaluate the impact of using appliances' load data, iterative ResBlocks as well as other factors for the proposed approach.