Computed tomography (CT) has been widely applied in medical diagnosis, industrial testing, and other fields. Recently, parallel translational computed tomography (PTCT) was proposed, in which the source and the detector were translated in parallel and opposite directions for data collection, featuring a simple structure, flexible applications, and low costs. In this paper, derivation-Hilbert transform-backprojection for PTCT (PTCT-DHB) based on Radon inverse transform was proposed for image reconstruction. Compared with the conventional algorithm of filtered backprojection for PTCT (PTCT-FBP), the proposed algorithm decomposed a ramp filter into two steps: derivation and Hilbert transform, which improved the noise resistance. Furthermore, a PTCT experimental system was established, and numerical simulations and practical experiments were performed. The results show that in comparison with the PTCT-FBP algorithm, the root mean squared error value of the images reconstructed by the PTCT-DHB algorithm is reduced by 0.0108, the peak signal-to-noise ratio value is increased by 4.437, and the structural similarity value is increased by 0.0041. The PTCT-DHB algorithm can effectively suppress high-frequency noise and quickly reconstruct high-quality CT images.