Progress on the fusion-fission hybrid reactor (FFHR) brings fusion a viable energy source in foreseeable future. Energy multiplication in a FFHR makes a much easier prerequisite for the fusion reaction than a fusion reactor. The molten salt reactor has advantages on heat transfer and post-processing of the spent fuels. A fission blanket made of molten salt was studied for the FFHR. The molten salt consists of F-Li-Be, with nuclear fuels dissolved in it. When thorium-uranium-plutonium fuels were added into a F-Li-Be molten salt zone with a component of 71% LiF -2% BeF2 -13.5% ThF4 -8.5% UF4 -5% PuF3, the appropriate blanket energy multiplication factor and TBR can be obtained. Two different molten salt models (Single molten salt zone model and multi molten salt zone model) were designed and compared in this study. The changes in blanket multiplication factor, M, and the tritium breeding ratio, TBR, during burnup life are investigated. The burnup analysis of the molten salt blanket was carried out by the COUPLE2 code. Through the burnup analysis, the breeding of the fissile fuel 233U and the transmutation of the minor actinides were also studied.