In this paper, we proposed an innovative encoder‐decoder structure with a convolution long short‐term memory (ED‐ConvLSTM) network to forecast global total electron content (TEC) based on the International GNSS Service (IGS) TEC maps from 2005 to 2018 with 1‐hr time cadence. The ED‐ConvLSTM model is used to forecast TEC maps 1–7 days in advance through iterations. To investigate the model's performance, we compared the model with International Reference Ionosphere (IRI2016) model in 2014 and 2018, and compared the model with 1‐day Beijing University of Aeronautics and Astronautics (BUAA) model in 2018. The results show that our 7‐day ED‐ConvLSTM model (ED‐ConvLSTM model that forecasts 7 days in advance) outperforms IRI2016 in 2014 and 2018, and our 5‐day ED‐ConvLSTM model (ED‐ConvLSTM model that forecasts 5 days in advance) outperforms 1‐day BUAA model. Furthermore, the root mean square error (RMSE) from the 1‐day ED‐ConvLSTM model with respect to the IGS TEC maps decreases by 51.5% and 43%, respectively, in 2014 and 2018 compared with that from IRI2016 model. The RMSE from the 1‐day ED‐ConvLSTM model is 20.3% lower than that from the 1‐day BUAA model in 2018. In addition, our model has the highest RMSE in the Equatorial Ionospheric Anomaly (EIA) region, but can roughly predict the features and locations of EIA. However, the model fails to forecast localized TEC enhancement and the sudden ionospheric response to the geomagnetic storms. Overall, the model shows competitive performance in medium‐term global TEC maps prediction during geomagnetic quiet periods.