In this paper, we have investigated the influence of peculiarities of the normal-state energy spectrum structure in high-temperature superconductors on the temperature dependences of the Hall coefficient, RH. Methods for accounting different specific features of the charge-carrier system when approximating the differential Hall conductivity function were proposed and used for simulating the RH(T) dependences in the framework of a narrow-band model. Simulation results show the Hall coefficient to be most sensitive to the existence of an asymmetry of the dispersion law. Taking this property into account one can obtain the calculated RH(T) curves corresponding well to the experimental ones observed for samples of the Y-based system with different deviations from the stoichiometric composition. This finding corresponds well to results obtained previously when analyzing the Nernst coefficient behavior in the same system and should be used for a further development of the approach to the joint quantitative analysis of the normal-state electron transport in high-temperature superconductors.