The rapid development of wireless networks makes it more convenient for people to enjoy high quality multimedia. However, video applications are throughput-demanding, and relatively, radio resource always seems insufficient. Hence, a distributed algorithm is designed in this paper to allocate the limited wireless resource among multiple users for video streaming. In order to specify multimedia service from other ordinary data transmission, the QoE-oriented utility function is considered first. Then, a potential game model is formulated and all the video receivers can update their rate strategies with very little information exchange. By this kind of updating, the bandwidth allocation could be achieved intelligently. The algorithm converges to a set of correlated equilibria. Numeric simulation results indicate that it brings remarkable benefits to both the resource provider and the video users.