When the multiple video sources are transmitted together through the channel of fixed bandwidth, an efficient picture quality control is necessary. This paper presents a joint picture quality control method to satisfy the user requirement by priority among the video sources. The better picture quality is assigned to the source of higher priority compared to lower priority. We obtain the bitrate for each source to have a required distortion level among the sources by using an approximate distortion-bitrate model for simple implementation. It is shown by simulation that the proposed bandwidth allocation method can keep almost the user-required picture quality among the sources in comparison to an independent bandwidth allocation method.