Abstract: FDK algorithm is widely used in computed tomography. However, the traditional rebin FDK algorithm heavily consumes memories, thus the reconstruction efficiency is low. Aiming to solve the problem, a selective projection-rebin FDK algorithm is proposed in this paper. By analyzing the geometrical relationship between the original projections and rebined ones, the least amount of cone-beam projections during each round of data rearrangement is derived. Circular queue is used to selectively load certain frames of cone-beam projections, which substantially reduces the memory-consumption. Based on graphic processing unit, the new algorithm is optimized for its parallelism performance, and the speed of the parallel method is boosted significantly. Experiments for the reconstruction of 512³ are performed to verify the effectiveness of the algorithm. Without loss of reconstruction accuracy, its memory consumption is reduced to 1/3 and 1/5 of the traditional for simulation data and real data respectively. The new algorithm, reducing the memory-consumption substantially, is the development of traditional rebin FDK algorithm, and it solves the problem of reconstruction for mass projections.