Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) inherently suffers from various errors. Many previous works employed Geoscience Laser Altimeter System onboard the Ice, Cloud, and land Elevation Satellite (ICESat/GLAS) data to assess and enhance SRTM DEM accuracy. Nevertheless, data coregistration between the two datasets was commonly neglected in their studies. In this paper, an automated and simple three dimensional (3D) coregistration method (3CM) was introduced to align the 3-arc-second SRTM (SRTM3) DEM and ICESat/GLAS data over Jiangxi province, China. Then, accuracy evaluation of the SRTM3 DEM using ICESat/GLAS data with and without data coregistration was performed on different classes of terrain factors and different land uses, with the purpose of evaluating the importance of data coregistration. Results show that after data coregistration, the root mean square error (RMSE) and mean bias of the SRTM3 DEM are reduced by 14.4% and 97.1%, respectively. Without data coregistration, terrain aspects with a sine-like shape are strongly related to SRTM3 DEM errors; nevertheless, this relationship disappears after data coregistration. Among the six land uses, SRTM3 DEM produces the lowest accuracy in forest areas. Finally, by incorporating land uses, terrain factors and ICESat/GLAS data into the correction models, the SRTM3 DEM was enhanced using multiple linear regression (MLR), back propagation neural network (BPNN), generalized regression NN (GRNN), and random forest (RF), respectively. Results exhibit that the four enhancement models with data coregistration obviously outperform themselves without the coregistration. Among the four models, RF produces the best result, and its RMSE is about 3.1%, 2.7% and 11.3% lower than those of MLR, BPNN, and GRNN, respectively. Moreover, 146 Global Navigation Satellite System (GNSS) points over Ganzhou city of Jiangxi province were used to assess the accuracy of the RF-derived SRTM3 DEM. It is found that the DEM quality is improved and has a similar error magnitude to that relative to the ICESat/GLASS data.