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When the multiple video sources are transmitted together through the channel of fixed bandwidth, an efficient joint bandwidth allocation is necessary. This paper presents a joint bandwidth allocation method to satisfy the user requirements that the bandwidths for each sources are assigned to allow differentially the certain picture quality levels according to their priorities. We first find a model of distortion and bitrate for the multiplexing system of multiple sources. Then we obtain the bitrate for each source to keep the required distortion level among the sources by using approximate model parameters for simple implementation. It is shown by simulation that the proposed bandwidth allocation method can keep almost the user-required picture quality level among the sources in comparison to an independent bandwidth allocation method.