Data broadcasting is independent of client arrival rate, and thus it is very suitable to transmit popular videos that interest many clients at a particular period of time. One broadcasting method (called periodic broadcasting) is to partition a video into segments, which are then simultaneously broadcast on several data channels. Once clients want to watch the video, they download the segments from these channels. Specially, the skyscraper broadcasting (SkB), client-centric approach (CCA), greedy disk-conserving broadcasting (GDB) schemes were proposed to support a client with a small bandwidth. This paper presents a limited-client-capability broadcasting (LCCB) scheme, which achieves small waiting time, bandwidth consumption, and buffer demand on the client side. In comparison with SkB, CCA, and GDB, LCCB gains smaller waiting time. Extensive simulation results indicate that LCCB also requires lower client buffer spaces than SkB, CCA, and GDB.