This manuscript proposes a method for characterizing the complex permittivity of the human finger skin based on an open-ended waveguide covered with a thin dielectric sheet at sub-terahertz frequencies. The measurement system is initially analyzed through full-wave simulations with a detailed finger model. Next, the model is simplified by replacing the finger with an infinite sheet of human skin to calculate the forward electromagnetic problem related to the permittivity characterization. Following this, a radial basis network is employed to train the inverse problem solver. Finally, the complex permittivities of finger skins are characterized for 10 volunteers. The variations in complex relative permittivity across different individuals and skin regions are analyzed at 140~GHz, revealing a maximum deviation of $\pm 0.7$ for both the real and imaginary parts. Repeated measurements at the same location on the finger demonstrate good repeatability with a relative estimation uncertainty $<\pm 1\%$.