Terahertz (THz) spectroscopy and imaging of biomedical samples is expected to be an important application of THz analysis techniques. Identification and localization of tumor tissue, imaging of biological samples, and analysis of DNA by THz spectroscopy have been reported. THz time-domain spectroscopy (TDS) is useful for obtaining the refractive index over a broad frequency range. However, THz-TDS spectra of fresh tissue samples are sensitive to procedures such as sample preparation, and a standardized measurement protocol is required. Therefore, in this work, we establish a protocol for measurements of THz spectra of fresh tissue and demonstrate reliable detection of rat brain tumor tissue. We use a reflection THz-TDS system to measure the refractive index spectra of the samples mounted on a quartz plate. The tissue samples were measured immediately after sectioning to avoid sample denaturalization during storage. Special care was taken in THz data processing to eliminate parasitic reflections and reduce noise. The error level in our refractive index measurements was as low as 0.02 in the frequency range 0.8–1.5 THz. With increasing frequency, the refractive index in the tumor and normal regions monotonically decreased, similarly to water, and it was 0.02 higher in the tumor regions. The spectral data suggest that the tumor regions have higher water content. Hematoxylin-eosin stained images showed that increased cell density was also responsible for the observed spectral features. A set of samples from 10 rats showed consistent results. Our results suggest that reliable tumor detection in fresh tissue without pretreatment is possible with THz spectroscopy measurements. THz spectroscopy has the potential to become a real-time in vivo diagnostic method.