Bioelectrical impedance spectroscopy is a noninvasive, label-free and quantitative detection technology, which has great advantages in the physiological and pathological analysis of biological cells and tissues. In this paper, the relationship between the electrical properties of a single cell and its structure is studied by numerical simulation. Moreover, experiments are conducted to verify the simulation results. For simulation, three single cell models are used to express its structure. Among of the three models, No Shell Model (NS) is proposed in this paper to study the influence of cell membrane on bioelectrical impedance spectroscopy. In addition, the effects of cell type, cell membrane and cell nucleus on its electrical properties are studied by simulation based on Single Shell Model (SS) and Two Shell Model (TS). The simulation results show that: 1) the electrical characteristics of cells can reflect its structure, therefore, the cell type can be accurately distinguished by its electrical characteristics; 2) the high frequency part of the Cole-Cole Plot is caused by ionic polarization of cytoplasm or extracellular fluid, and the low frequency part of the Cole-Cole Plot is caused by interface polarization between cell membrane and the extracellular fluid; 3) the influence of cell nucleus size on impedance measurement is mainly in the low frequency range, which is caused by the polarization of the interface between cell nucleus and intracellular fluid, and when the nucleocytoplasmic ratio is less than 0.25, the effect of nuclear size on impedance analysis could be ignored. Finally, an experiment was conducted on 20% yeasts suspension with different activity to verify the simulation results. It is known that the cell membranes of dead yeasts are destroyed, however, living yeasts have completed cell structures. The structure difference between living and dead yeast is distinguished by electrical impedance spectroscopy through numerical simulation. The experimental results are consistent with the simulation results, which verifies the fact that the high frequency part of the Cole-Cole Plot is caused by ionic polarization of cytoplasm or extracellular fluid, and the low frequency part of the Cole-Cole Plot is caused by interface polarization between cell membrane and the extracellular fluid.