To address the scalability issue in video-on-demand systems, many broadcasting schemes have been proposed to date. The major performance parameters of such a broadcasting scheme are the server broadcast bandwidth, the user bandwidth and the user’s initial waiting time. The broadcasting schemes with the least server bandwidth requirement currently known require the same bandwidth on the user side as that on the server side. We propose a new broadcast scheme, named Generalized Fibonacci Broadcasting (GFB), to address the issue of limiting the user-side bandwidth requirement. For any given combination of the server and user bandwidths, GFB can always achieve the least user waiting time among all the currently known broadcasting schemes. Furthermore, it would be very easy to implement GFB.