Due to the limitation of earth observation technology, the existing global Digital Elevation Model (DEM) datasets usually contain information of vegetation, buildings, and other non-ground objects. Especially in forested areas, the DEM data usually cannot describe the bare-earth surface precisely and show large systematic deviations. This study proposes a Back Propagation Neural Network (BPNN) model that takes into account the spatial autocorrelation of elevation to reduce the errors of bare-earth DEM in forested areas. This model first fits the optimal semivariogram to determine the spatial variation of elevation and takes the elevation points within the variation range from a target point as the optimal spatially autocorrelated neighborhood. Then, we train the BPNN model by using the terrain factors (i.e., slope, aspect, and terrain undulation), vegetation factors (i.e., vegetation height and vegetation coverage), and elevation points within the range of variation as the influencing factors, and using the elevation difference between DEM and Light Detection And Ranging (LiDAR) DEM as the predicted value. Finally, the trained model is used to correct the DEM in different forested areas. In order to verify the practicability and efficiency of the model, this paper takes the DEM products including SRTM1, AW3D30, and TanDEM-X (TDX) 90 of four types of forests (evergreen broad-leaved forest, evergreen coniferous forest, mixed forest, and deciduous broad-leaved forest) as the research objects, and trains the BPNN model respectively for each forest type. The correction result is compared with BPNN trained with all four types of forest data (BPNN-T), BPNN trained without terrain factors (BPNN-W), BPNN trained without spatial autocorrelation of elevation (BPNN-R), and multiple linear regression model (MLR). The results show that: (i) The BPNN model significantly improves the accuracy of DEM in the four forests, with the Mean Error (ME) close to 0-1 m and the Root Mean Square Errors (RMSE) reduced by 46%~70%; (ii) The aspect has the largest influence on the DEM correction for TDX90 while has little influence on SRTM1 DEM correction. Before and after correction, the RMSE of each DEM increases with the increase of slope and relief; (iii) The DEM error increases with the increase of vegetation height and vegetation coverage before correction, but this trend disappears after correction, indicating that BPNN effectively eliminates the impact of vegetation on bare ground DEM; (iv) BPNN has the highest prediction accuracy, followed by BPNN-T, MLR, and BPNN-W. And BPNN-R has the worst prediction accuracy. Therefore, the accuracy of DEM can be significantly improved by fully considering terrain factors and spatial autocorrelation of elevation for different forest types.