We present new results demonstrating the capability of performing computed tomography (CT) using broadband Bessel terahertz (THz) beams. Nondiffractive beams such as these exhibit propagation-invariant lines of focus with an extended depth-of-field compared to conventional Gaussian beams. Using this property, we demonstrate a considerable improvement in the 3D reconstruction image of a synthetic sample through the backprojection algorithm. Only when THz Bessel beams are used, a full reconstruction of the object structure is made. Moreover, we use phase-contrast mechanism which improves the spatial resolution and reconstructed images. Our results highlight the potential in using nondiffractive Bessel beams to significantly improve 3D-image reconstruction of THz CT.