IPTV services are typically featured with a longer channel changing delay compared to the conventional TV systems. The major contributor to this lies in the time spent on intraframe (I-frame) acquisition during channel changing. Currently, most widely adopted fast channel changing (FCC) methods rely on promptly transmitting to the client (conducting the channel changing) a retained I-frame of the targeted channel as a separate unicasting stream. However, this I-frame acceleration mechanism has an inherent scalability problem due to the explosions of channel changing requests during commercial breaks. In this paper, we propose a fairness-based admission control (FAC) scheme for the original I-frame acceleration mechanism to enhance its scalability by decreasing the bandwidth demands. Based on the channel changing history of every client, the FAC scheme can intelligently decide whether or not to conduct the I-frame acceleration for each channel change request. Comprehensive simulation experiments demonstrate the potential of our proposed FAC scheme to effectively optimize the scalability of the I-frame acceleration mechanism, particularly in commercial breaks. Meanwhile, the FAC scheme only slightly increases the average channel changing delay by temporarily disabling FCC (i.e., I-frame acceleration) for the clients who are addicted to frequent channel zapping.