As a result of improvements in wireless communication technologies, a multimedia data streaming service can now be provided for mobile clients. Since mobile devices have low computing power and work on a low network bandwidth, a transcoding technology is needed to adapt the original streaming media for mobile environments. However, wireless networks have variable bandwidths depending on the movement of clients and the communication distance from Access Point (AP). These characteristics make it hard to support stable Quality of Service (QoS) streams for mobile clients. In this paper, a target transcoding bit-rate decision algorithm is proposed to provide stable QoS streams for mobile clients. In our experiments, the proposed algorithm provides seamless streaming media services based on the network adaptive bit rate control and reduces transmission failure.