A high-quality leaf-area index (LAI) is important for land surface process modeling and vegetation growth monitoring. Although multiple satellite LAI products have been generated, they usually show spatio-temporal discontinuities and are sometimes inconsistent with vegetation growth patterns. A deep-learning model was proposed to retrieve time-series LAIs from multiple satellite data in this paper. The fusion of three global LAI products (i.e., VIIRS, GLASS, and MODIS LAI) was first carried out through a double logistic function (DLF). Then, the DLF LAI, together with MODIS reflectance (MOD09A1) data, served as the training samples of the deep-learning long short-term memory (LSTM) model for the sequential LAI estimations. In addition, the LSTM models trained by a single LAI product were considered as indirect references for the further evaluation of our proposed approach. The validation results showed that our proposed LSTMfusion LAI provided the best performance (R-2 = 0.83, RMSE = 0.82) when compared to LSTMGLASS (R-2 = 0.79, RMSE = 0.93), LSTMMODIS (R-2 = 0.78, RMSE = 1.25), LSTMVIIRS (R-2 = 0.70, RMSE = 0.94), GLASS (R-2 = 0.68, RMSE = 1.05), MODIS (R-2 = 0.26, RMSE = 1.75), VIIRS (R-2 = 0.44, RMSE = 1.37) and DLF LAI (R-2 = 0.67, RMSE = 0.98). A temporal comparison among LSTMfusion and three LAI products demonstrated that the LSTMfusion model efficiently generated a time-series LAI that was smoother and more continuous than the VIIRS and MODIS LAIs. At the crop peak growth stage, the LSTMfusion LAI values were closer to the reference maps than the GLASS LAI. Furthermore, our proposed method was proved to be effective and robust in maintaining the spatio-temporal continuity of the LAI when noisy reflectance data were used as the LSTM input. These findings highlighted that the DLF method helped to enhance the quality of the original satellite products, and the LSTM model trained by the coupled satellite products can provide reliable and robust estimations of the time-series LAI.