Smoothing is a transmission plan where variable rate video data is converted to a constant bit rate stream. Among them are CBA, MCBA, MVBA and others. However, these smoothing algorithms produce a transmission plan where extra bandwidth in server is not considered. This may cause difficulty in providing videos to many clients in a server. In this paper, we propose the smoothing algorithm with monotonic transmission rate increase and abrupt transmission rate decrease, in order to provide videos to as many clients in server with limited network bandwidth as possible. In order to show the performance of our proposed algorithm, various evaluation factors were used such as the maximum number of clients, the average number of clients, and so on. Experiments demonstrated that the proposed algorithm outperformed other algorithms in evaluation factors such as the maximum number of clients and the average number of clients.