Previously, we described a social media cloud computing service environment (SMCCSE). This SMCCSE supports the development of social networking services (SNSs) that include audio, image, and video formats. A social media cloud computing PaaS platform, a core component in a SMCCSE, processes large amounts of social media in a parallel and distributed manner for supporting a reliable SNS. Here, we propose a Hadoop-based multimedia system for image and video transcoding processing, necessary functions of our PaaS platform. Our system consists of two modules, including an image transcoding module and a video transcoding module. We also design and implement the system by using a MapReduce framework running on a Hadoop Distributed File System (HDFS) and the media processing libraries Xuggler and JAI. In this way, our system exponentially reduces the encoding time for transcoding large amounts of image and video files into specific formats depending on user-requested options (such as resolution, bit rate, and frame rate). In order to evaluate system performance, we measure the total image and video transcoding time for image and video data sets, respectively, under various experimental conditions. In addition, we compare the video transcoding performance of our cloud-based approach with that of the traditional frame-level parallel processing-based approach. Based on experiments performed on a 28-node cluster, the proposed Hadoop-based multimedia transcoding system delivers excellent speed and quality.