A terahertz (THz) fan-beam computed tomography (CT) system using a 0.3 THz continuous-wave sheet beam is proposed. The diffraction-free sheet beam expands in a fan shape in only one direction and provides propagation-invariant focal lines and extended the depth-of-field. The fan-beam CT based on this beam is the second-generation THz CT. It breaks the conventional 4-f symmetric structure of THz CT using the parallel beam. The fan-beam THz CT allows for use with a linear array detector, which reduces the time required to collect data. To demonstrate its feasibility for three-dimensional (3D) imaging, the 3D structure of a metal rod packed in a carton is reconstructed with the support of the system. The results show that the object's internal structure can be obtained by this new THz CT system while retaining the geometrically magnified features of the cross-sectional structure. The results of our research provide a template for the second-generation THz CT system, which provides an additional method for nondestructive testing.