Transcoding in the wireless mobile network is an important mechanism that reduces the delay time and improves the stream processing capacity. Wireless mobile streaming media services, however, have such problems as congestion, interference and delay due to narrow network bandwidth and limited resources. These problems degrade not only Quality of Service (QoS) but also responsiveness of the streaming media service. To solve this problem, this paper proposes a object version transcoding method. The proposed method analyzes the object versions to construct the transcoding graph. This paper utilizes a reference rate-based control function for an efficient streaming, and measures MVDS(Multiple Version Delay Saving) for an efficient delay savings. The simulation results show that the proposed mechanism achieves improved performance in delay rate and cache hit rate compared with those of other existing methods.