In this letter, a terahertz (THz) tomography system based on a quantum cascade laser (QCL) and a quantum-well photodetector (QWP) is demonstrated. The QCL provides a relatively high power (a few microwatts) in a continuous-wave mode at 3.9 THz as a light source, and the QWP provides a narrow response range from 3 to 7 THz with a calibrated peak response of 0.5 A/W under background-limited performance. We employ the widely-used filtered back projection (FBP) and algebraic reconstruction algorithms for terahertz tomography technology. The reconstructed cross-sectional image of a sample has successfully revealed the internal and the external structures with a resolution of around 1.5 mm. This experiment demonstrates that the terahertz QCL and the photodetector are potentially useful for terahertz tomography applications.