In daily natural gas consumption forecasting, the accuracy of forecasting models is vulnerably affected by the noise data in historical time series. Singular spectrum analysis (SSA) is often introduced into hybrid models for denoising. However, as a deterministic-based algorithm, SSA does not give good results when a time series is contaminated with a high noise level. Considering this fact, this paper proposes an improved SSA (ISSA) that modifies the determination method of subseries selection in the reconstruction stage of SSA. Combining ISSA with long short-term memory (LSTM), a novel hybrid model, ISSA-LSTM, is thus developed. Additionally, for validating the robustness and superiority of ISSA-LSTM, the historical datasets of four representative cities located in three climate zones are collected as the training and testing datasets, and a comparison of ISSA-LSTM with five advanced models is performed. The results reveal that SSA would generate negative values when time series close to zero and the contribution of SSA in improving the forecasting accuracy of LSTM is insignificant. In contrast, ISSA avoids generating negative values and reduces the mean absolute range normalized error (MARNE) of LSTM by a range of 0.86-11.86%. Among the models, ISSA-LSTM achieves the best performance and its MARNEs for London (temperate zone), Melbourne (subtropical zone), Karditsa (subtropical zone), and Hong Kong (tropical zone) are 4.68%, 5.72%, 5.76%, and 14.10%, respectively. The MARNE of the tropical city is higher than that of others, which is caused by the complex natural gas consumption pattern of itself.