Monte Carlo simulation has been used to study magnetic and thermodynamic properties of a ferrimagnetic mixed-spin (1, 3/2) Ising fullerene-like X20 structure with embedded metal atom. Under the influence of the anisotropy and the concentration of surface shell atom, the system tends to show the multiple stable saturation values of magnetization (M = 0.91, 0.85, 0.77, 0.64, 0.50 and 0.023) and the values of intermediate metastable magnetization (M = 0.88, 0.76 and 0.60) at zero temperature. The blocking temperature T
B
becomes higher by decreasing the anisotropies (∣D
C
∣, ∣D
S
∣), or increasing the exchange coupling ∣J
CS
∣, the magnetic field h and the concentration of surface shell atom P
S
. Some interesting phenomena have been found such as the double-loop hysteresis behavior for the relatively large values of ∣D
S
∣ (≥2.0), originating from the competition between different physical parameters.