Abstract: In a traditional cone-beam CT system,the cost of product and computation is very high.In this paper,we discuss a transversely truncated cone-beam X-ray CT system with a reduced size detector positioned off-center,in which X-ray beams only cover half of the object.The reduced detector size cuts the cost and the X-ray dose of the CT system.The existing reconstruction algorithm is to get the parallel projections in 180 degrees using rebinding method.Then,it uses filtered-back projection(FBP) algorithm to get the final images.But,rebinding will introduce blurring and reduce image resolution.Hence,we develop a BPF-type direct back projection algorithm.Different from the traditional rebinding methods,our algorithm directly back projects the pretreated projection data without rebinding.This makes the algorithm compact and computationally more efficient.Finally,some numerical simulations are done to validate the proposed algorithm.