Anomaly　detection　offers　a　powerful　approach　to　identifying　unusual　activities　and　uncommon　behaviors　in　real-world　video　scenes.　At　present,　convolutional　neural　networks　(CNN)　have　been　widely　used　to　tackle　anomalous　events　detection,　which　mainly　rely　on　its　stronger　ability　of　feature　representation　than　traditional　hand-crafted　features.　However,　massive　video　data　and　high　cost　of　CNN　model　training　are　a　challenge　to　achieve　satisfactory　detection　results　for　resource-limited　users.　In　this　article,　we　propose　a　secure　video　anomaly　detection　framework　(SecureAD)　based　on　CNN.　Specifically,　we　introduce　additive　secret　sharing　to　design　several　calculation　protocols　for　achieving　safe　CNN　training　and　video　anomaly　detection.　Besides,　we　propose　a　Bloom　filter　based　fine-grained　access　control　policy　to　authenticate　legitimate　users,　without　leaking　the　privacy　of　raw　personal　attributes.　In　addition,　edge　computing　instead　of　cloud　computing　is　integrated　into　the　architecture　to　reduce　response　time　between　servers　and　users　in　an　outsourced　environment.　Finally,　we　prove　that　the　proposed　SecureAD　achieves　secure　video　anomaly　detection　without　compromising　the　privacy　of　the　related　data.　Also,　the　simulation　results　demonstrate　the　effectiveness　and　security　of　our　SecureAD.