Multiple　multi-dimensional　data　streams　are　ubiquitous　in　the　modern　world,　such　as　IoT　applications,　GIS　applications　and　social　networks.　Detecting　anomalies　in　such　data　streams　in　real-time　is　an　important　and　challenging　task.　It　is　able　to　provide　valuable　information　from　data　and　then　assists　decision-making.　However,　exiting　approaches　for　anomaly　detection　in　multi-dimensional　data　streams　have　not　properly　considered　the　correlations　among　multiple　multi-dimensional　streams.　Moreover,　for　multi-dimensional　streaming　data,　online　detection　speed　is　often　an　important　concern.　In　this　paper,　we　propose　a　fast　yet　effective　anomaly　detection　approach　in　multiple　multi-dimensional　data　streams.　This　is　based　on　a　combination　of　ideas,　i.e.,　stream　pre-processing,　locality　sensitive　hashing　and　dynamic　isolation　forest.　Experiments　on　real　datasets　demonstrate　that　our　approach　achieves　a　magnitude　increase　in　its　efficiency　compared　with　state-of-the-art　approaches　while　maintaining　competitive　detection　accuracy.