As an effective drag reduction control method, porous media have attracted extensive attention in various engineering fields. In this paper, the large eddy simulation method is used to study the flow problem around a cylinder with and without porous media covering at subcritical Reynolds numbers. The drag reduction characteristics and the mechanism of a cylinder covered with porous media were studied. The results of the aerodynamic drag coefficient show that when the Reynolds number is 5.6 × 104 and when the porous media are arranged on the leeward side of the cylinder at an azimuth angle of 270°, the drag reduction rate is the largest, reaching 8.53%. The flow field results indicate that after porous media covering, the large-scale wake vortex shedding was effectively suppressed, the vortex shedding frequency was reduced, the vortexes in the wake area became thinner and longer, and the vorticity decreased. It is confirmed that porous media can stabilize the wake shear layer and suppress the unsteady vortex motion in the wake. Meanwhile, airflow can penetrate the porous media, leading to velocity slip at the interface between the porous media and the airflow, making the free shear layer more stable, and strengthen the wake vortex.