Home　range　estimation　is　the　basis　of　ecology　and　animal　behavior　research.　Some　popular　estimators　have　been　presented;　however,　they　have　not　fully　considered　the　impacts　of　terrain　and　obstacles.　To　address　this　defect,　a　novel　estimator　named　the　density-based　fuzzy　home　range　estimator　(DFHRE)　is　proposed　in　this　study,　based　on　the　active　learning　method　(ALM).　The　Euclidean　distance　is　replaced　by　the　cost　distance-induced　geodesic　distance　transformation　to　account　for　the　effects　of　terrain　and　obstacles.　Three　datasets　are　used　to　verify　the　proposed　method,　and　comparisons　with　the　kernel　density-based　estimator　(KDE)　and　the　local　convex　hulls　(LoCoH)　estimators　and　the　cross　validation　test　indicate　that　the　proposed　estimator　outperforms　the　KDE　and　the　LoCoH　estimators.