Most algorithms of smoothing schedule compute the required bit rate of the video transmission to satisfy all the transmitted data. MPEG-4 with Fine Grained Scalability supports partial data dropping to adapt to available bandwidth network. In this paper, our proposed dropping algorithm can adjust the transmitting data to fit the available bit rate. Our algorithm is based on the minimum variance bandwidth allocation algorithm proposed by Salehi et al. to compute the bit rates such that still ensuring that the buffer never underflows and overflows for MPEG-4 FGS streams under the limited bandwidth resource. When the transmitted bit rate is no greater than the bit rate of all the layers in MPEG-4, our proposed algorithm can drop partial data to adapt the available bandwidth and to tolerate a userdefined dropping ratio. The experimental results show that the peak rate, the number of changes, and the ratio of total dropping data for four test sequences with different content characteristic are varied by the buffer sizes and the tolerable dropping ratios. We found that the algorithm can reduce the peak rate and the number of changes when the transmitted data are dropped by tolerable dropping ratio, especially on the video sequences with the larger variable sizes of consecutive frames.