Ionospheric Total Electron Content (TEC) prediction has important reference significance for the accuracy of global navigation satellite systems (GNSS) based global positioning system, satellite communications and other space communications applications. In the study, an available prediction model of global IGS-TEC map is established based on testing several different LSTM-based algorithms. We find that Multi-step auxiliary algorithm based prediction model performs the best. It can precisely predict the global ionospheric IGS-TEC in the next 6 days (the MAD and RMSE are 2.485 and 3.511 TECU, respectively). Then, the autoencoder network algorithm is adopted to construct an assimilation model that transforming IGS-TEC map to MIT-TEC map. In order to judge the validity of the assimilation model, the outputs of the assimilation model are evaluated and compared with the IRI2016 model in four different geomagnetic storm events. It seems that the assimilation model can accurately forecast MIT-TEC by inputting the predicted IGS-TEC value. The performance of assimilation model for the predicting MIT-TEC is better than that of IRI2016.