Monte Carlo simulation has been used to study the behavior of the magnetization plateaus of the bi-layer graphyne like-structure with spin-2 and spin-5/2 by varying different physical parameters. We start by examining the ground state phase diagrams for zero temperature to establish the stable phases. Besides, we investigate the behavior of the magnetization plateaus for different physical parameters and we explore the critical (h_C) and the saturation (h_S) magnetic fields. Indeed, our Monte Carlo simulations, have been performed to deduce the ground state phase diagrams for t = 0 and the magnetization plateaus for t > 0 for the bi-layer graphyne like-structure in different planes of the reduced physical parameters (d, t, ${\mathrm{r}}_2$ and ${\mathrm{r}}_1$). The results show that among 30 possible configurations only 18 can be stable. Besides, the system shows multiple magnetization plateaus behaviors for low temperature. The behavior of the critical (h_C) and the saturation (h_S) magnetic fields by varying different physical parameters has been outlined.