A three-dimensional (3D) terahertz (THz) computed tomography system with a THz quantum cascade laser as the source and a quantum well photodetector as the receiver is demonstrated. By utilising the algebraic reconstruction technique for image reconstruction, both the external and internal structures of the cross-section are revealed. The iterative algorithm not only reduces the projections, but also provides good suppression of the beam hardening effect. Finally, the 3D image is built by stacking the images at different heights.Introduction: In the field of three-dimensional (3D) imaging, computed tomography (CT) is a significant technique that is first applied in the X-ray frequency band, which reveals the cross-sectional image of an object by using the transmitted signals and image reconstruction algorithms. However, the high-power of X-rays limits its utilisation because of the dangerous ionising effect and the low contrast for soft materials. Compared with X-rays, terahertz (THz) radiation possesses low photon energy, a broad spectra range and moderate penetration for many packaging materials. Since the first THz CT demonstration was reported in 2002 by Ferguson et al.[1], it has been proposed for the 3D imaging of different objects in the industrial, pharmaceutical to biomedical fields [2]. For the CT technique, choosing an appropriate reconstruction algorithm is of great importance. The most efficient and widely used algorithm of CT reconstruction is the filter back-projection (FBP) method, which is based on the Radon inverse transformations from the projection data. In practice, FBP suffers from several disadvantages such as beam hardening, noise sensitivity and image aberration in the case of an insufficient number of angle samplings [3]. Consequently, the iterative reconstruction methods have been proposed for CT reconstruction, such as the algebraic reconstruction technique (ART) [4], the simultaneous iterative reconstruction technique (SIRT) [5] and ordered subsets expectation maximisation (OSEM) [6]. These algorithms have been applied in X-ray CT previously, but few in THz CT.On the hardware side, the THz quantum-cascade laser (QCL) is one of the most important THz solid-state sources, having high output power and a compact structure [7], and the THz quantum-well photodetector (QWP) is a very promising detector that has the characteristics of high sensitivity, a narrow response range and fast photoresponse [8]. In this Letter, we first present a THz 3D imaging system based on a THz QCL and a QWP, then reconstruct a cross-sectional image of the sample by the ART algorithm, and finally demonstrate the 3D reconstruction image and point out the places that need to be improved in the future.