A new Hopfield neural network (HNN) model for downscaling a digital elevation model in grid form (gridded DEM) is proposed. The HNN downscaling model works by minimizing the local semivariance as a goal, and by matching the original coarse spatial resolution elevation value as a constraint. The HNN model is defined such that each pixel of the original coarse DEM is divided into f × f subpixels, represented as network neurons. The elevation of each subpixel is then derived iteratively (i.e., optimized) based on minimizing the local semivariance under the coarse elevation constraint. The proposed HNN model was tested against three commonly applied alternative benchmark methods (bilinear resampling, bicubic and Kriging resampling methods) via an experiment using both degraded and sampled datasets at 20-, 60-, and 90-m spatial resolutions. For this task, a simple linear activation function was used in the HNN model. Evaluation of the proposed model was accomplished comprehensively with visual and quantitative assessments against the benchmarks. Visual assessment was based on direct comparison of the same topographic features in different downscaled images, scatterplots, and DEM profiles. Quantitative assessment was based on commonly used parameters for DEM accuracy assessment such as the root mean square error, linear regression parameters m and b, and the correlation coefficient R. Both visual and quantitative assessments revealed the much greater accuracy of the HNN model for increasing the grid density of gridded DEMs.