Forecasting daily natural gas load accurately is difficult because it is affected by various factors. A large number of redundant factors existing in the original dataset will increase computational complexity and decrease the accuracy of forecasting models. This study aims to provide accurate forecasting of natural gas load using a deep learning (DL)-based hybrid model, which combines principal component correlation analysis (PCCA) and (LSTM) network. PCCA is an improved principal component analysis (PCA) and is first proposed here in this paper. Considering the correlation between components in the eigenspace, PCCA can not only extract the components that affect natural gas load but also remove the redundant components. LSTM is a famous DL network, and it was used to predict daily natural gas load in our work. The proposed model was validated by using recent natural gas load data from Xi’an (China) and Athens (Greece). Additionally, 14 weather factors were introduced into the input dataset of the forecasting model. The results showed that PCCA–LSTM demonstrated better performance compared with LSTM, PCA–LSTM, back propagation neural network (BPNN), and support vector regression (SVR). The lowest mean absolute percentage errors of PCCA–LSTM were 3.22% and 7.29% for Xi’an and Athens, respectively. On these bases, the proposed model can be regarded as an accurate and robust model for daily natural gas load forecasting.