In view of the lack of research on interpolation error and the difficulty in selecting interpolation methods for constructing mine digital elevation model ( DEM ) from airborne LiDAR ground point cloud data under complex terrain conditions in mines in southern Shanxi Province, three representative mine terrains in a mine in Changzhi City were taken as experimental objects, namely ridges, gullies and hilly farmland, and ground point cloud data were obtained by airborne LiDAR. Inverse Distance Weight ( IDW ), Ordinary Kriging ( OK ), Radial Basis Function ( RBF ), Natural Neighbor ( NN ) and Triangulated Irregular Network ( TIN ) interpolation methods are used to construct DEM under three terrains and study the error law. Firstly, the selection of interpolation parameters of IDW, RBF and OK interpolation methods is compared. Secondly, five interpolation methods of IDW, OK, RBF, NN and TIN are used to construct DEM under three terrains, and the relationship between interpolation error and point cloud density is tested. Finally, the ridge line and valley line are extracted from the DEM constructed by low density point cloud, and the accuracy of the five methods to describe the ridge line and valley line under low density point cloud is compared.The results show that : ( 1 ) In the three terrains, the optimal weight index is 2 in the IDW interpolation method ; in the RBF interpolation method, the thin plate spline function and the tension spline function are optimal ; in the OK interpolation method, the error of each sub-function is similar. When the point cloud density is less than 20 %, the DEM error is most affected by the point cloud density, and the IDW interpolation method has the largest change range. ( 3 ) When the point cloud density of the local surface is large enough, the point cloud density is 60 % -100 % in the experiment. The difference between the DEM errors constructed by the five interpolation methods is within 2cm and the interval is less affected by the point cloud density. ( 4 ) Under the condition of having less ground point cloud density, the experiment is 5 % of the point cloud density. The RBF interpolation method has the best accuracy in describing the ridge line and constructing the DEM under the ridge terrain. The OK interpolation method has the best accuracy in describing the valley line and constructing the DEM in the gully terrain. The NN interpolation method and the OK interpolation method have the best accuracy for the description of the scarp and the constructed DEM in the hilly farmland terrain. The research results can provide a basis for the construction of mine fine DEM under complex terrain.