The size of nerve cell is comparable to the wavelength of terahertz (THz) wave. In this work, a new concept of weak resonance effect of nerve cells is proposed. The permittivity of intracellular fluid is measured experimentally by using a THz-TDS system, and the relationship between the permittivity of nerve cells and the frequency is obtained by fitting the double Debye model. The propagation characteristics of THz waves in nerve cells are studied by finite difference time domain. The results show that when the dielectric constant of nerve cell is higher than that of the external medium, THz wave can be enhanced in the nerve cell. Meanwhile, as the dielectric constant of the external medium increases, the resonance will be close to the cell membrane. And it shows the focusing property of THz waves, as a convex lens does. The weak resonance effect is related to the dielectric constant of the background medium, and increases with the cell size and frequency increasing. These results provide a new model to explain the interaction between THz wave and nerve cells, contributing to the study of the transmission mechanism of THz wave in biological nervous system.