Complete high resolution geochemical maps are strongly needed for mineral exploration; however, the previously proposed methods for making geochemical maps have low accuracy. In this research, we propose a new algorithm called sample density based mixture interpolation (SADBAMIN) for high resolution geochemical map completion using remote sensing data. In the SADBAMIN algorithm, first, according to the measured copper data density on the map, the map is classified into two parts: the area for training (T area) and the area waiting to be predicted (P area). The two areas are classified by the edge of the data point set’s alpha shape. In the T area, a triangle area among three neighbourhood points is interpolated by using the kriging model. Then, remote sensing data, including advanced spaceborne thermal emission and reflection radiometer (ASTER) data, digital elevation model (DEM) data, and geophysics (magnetic) data, and copper geochemical data at all measured and partial randomly selected interpolated points are applied as training data to construct a random forest regression model. By considering the relationship between interpolation reliability and distance, a penalty on data selection probability of going into training data is given. Finally, by inputting the remote sensing data in the P area to the model, the copper data in this area can be obtained, and the completed map comprises these two parts. We use 16,000 measured points, 10-fold cross-validation, and root mean squared error (RMSE) for model evaluation. We achieved an RMSE of 293 ppm, while the RMSE of the previously proposed method is 347 ppm.