Most　of　the　current　intelligent　Internet　of　Things　(IoT)　products　take　neural　network-based　speech　recognition　as　the　standard　human-machine　interaction　interface.　However,　the　traditional　speech　recognition　frameworks　for　smart　IoT　devices　always　collect　and　transmit　voice　information　in　the　form　of　plaintext,　which　may　cause　the　disclosure　of　user　privacy.　Due　to　the　wide　utilization　of　speech　features　as　biometric　authentication,　the　privacy　leakage　can　cause　immeasurable　losses　to　personal　property　and　privacy.　Therefore,　in　this　paper,　we　propose　an　outsourced　privacy-preserving　speech　recognition　framework　(OPSR)　for　smart　IoT　devices　in　the　long　short-term　memory　(LSTM)　neural　network　and　edge　computing.　In　the　framework,　a　series　of　additive　secret　sharing-based　interactive　protocols　between　two　edge　servers　are　designed　to　achieve　lightweight　outsourced　computation.　And　based　on　the　protocols,　we　implement　the　neural　network　training　process　of　LSTM　for　intelligent　IoT　device　voice　control.　Finally,　combined　with　the　universal　composability　theory　and　experiment　results,　we　theoretically　prove　the　correctness　and　security　of　our　framework.