1. A speech recognition system using incremental device-based acoustic model adaptation comprising: a model selection module selecting an acoustic model of a multi-model tree by verifying and categorizing a device key transmitted from a user device; a model management module generating and incrementally adapting the multi-model tree by categorizing voice data based on a user device; and a speech recognition module performing speech recognition based on the acoustic model received from the model selection module and transmitting data of which reliability exceeds a predetermined threshold value to the model management module.