Monte Carlo simulation has been used in detail to study the step effect of the hysteresis loop for a ferrimagnetic mixed spin-2 and spin-5/2 Ising model on a honeycomb lattice. The results indicate that the hysteresis loops exhibit an obvious step effect and various shapes for different single-ion anisotropies and exchange couplings at very low temperature. Under a longitudinal magnetic field (h > 0 or h < 0), we have obtained 2S + 1 magnetic plateaus for different single-ion anisotropies at low temperature. The existence of triple and double hysteresis loop patterns has been found in the system. It is shown that the sublattice anisotropy and the interlayer exchange coupling strongly affect the coercivity of the system. The influence of the interlayer exchange couplings on the total magnetization, susceptibility, internal energy and specific heat with temperature are numerically examined in the absence of the longitudinal field.