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Video stream is converted to several formats to support the user's device, this conversion process is called video transcoding, which imposes high storage and powerful resources. With emerging of cloud technology, video stream companies adopted to process video on the cloud. Generally, many formats of the same video are made (pre-transcoded) and streamed to the adequate user's device. However, pre-transcoding demands huge storage space and incurs a high-cost to the video stream companies. More importantly, the pre-transcoding of video streams could be hierarchy carried out through different storage types in the cloud. To minimize the storage cost, in this paper, we propose a method to store video streams in the hierarchical storage of the cloud. Particularly, we develop a method to decide which video stream should be pre-transcoded in its suitable cloud storage to minimize the overall cost. Experimental simulation and results show the effectiveness of our approach, specifically, when the percentage of frequently accessed videos is high in repositories, the proposed approach minimizes the overall cost by up to 40 percent.