This paper proposes a new scheduling technique to play multimedia data streams in mobile terminals. The paper explores the characteristics of multimedia data streams , firstly. On basis of these characteristics, selection of specific data stream can be possible as well as transcoding protest. Our approach aims at reducing the early-stage delay time more effectively since it makes possible to select and transcodes some specific streams by employing a selection policy rather than transcoding all streams in the playing process Thus, this paper suggests a stream selection policy for the transcoding based on EPOB (End Point of Over Bandwidth). It aims to lower the required bandwidth of multimedia streams than the network bandwidth level and also to minimize early-stage delay time for multimedia streams, which is to be played in mobile terminals.