Terahertz waves provide a better contrast in imaging soft biomedical tissues than X-rays, and unlike X-rays, they cause no ionisation damage, making them a good option for biomedical imaging. Terahertz absorption imaging has conventionally been used for cancer diagnosis. However, the absorption properties of a cancerous sample are influenced by two opposing factors: an increase in absorption due to a higher degree of hydration and a decrease in absorption due to structural changes. It is therefore difficult to diagnose cancer from an absorption image. Phase imaging can thus be critical for diagnostics. We demonstrate imaging of the absorption and phase-shift distributions of 3.2 mm × 2.3 mm × 30-μm-thick human hepatocellular carcinoma tissue by continuous-wave terahertz digital in-line holography. The acquisition time of a few seconds for a single in-line hologram is much shorter than that of other terahertz diagnostic techniques, and future detectors will allow acquisition of meaningful holograms without sample dehydration. The resolution of the reconstructions was enhanced by sub-pixel shifting and extrapolation. Another advantage of this technique is its relaxed minimal sample size limitation. The fibrosis indicated in the phase distribution demonstrates the potential of terahertz holographic imaging to obtain a more objective, early diagnosis of cancer.