Understanding the interaction of graphene with cell membranes is crucial to the development of graphene-based biological applications and the management of graphene safety issues. To help reveal the key factors controlling the interaction between graphene and cell membranes, here we adopt the dissipative particle dynamics method to analyze the evolution of interaction force and free energy as the graphene-covered atomic force microscopy (AFM) probe indents across a lipid bilayer. The simulation results show that the graphene-covered AFM probe can cause severe deformation of the cell membrane which drives the lipid molecule to adsorb and diffuse at the surface of graphene. The breakthrough force and free energy are calculated to study the effects of the tip shape, size, and surface hydrophobicity on the piercing behaviors of graphene-covered AFM. In addition, the deformation of cell membrane can decrease the dependency of the breakthrough force on the tip shape. The analysis of surface functionalization suggests that the horizontal patterns on graphene can change the preferred orientation in the penetration process, but the vertical patterns on graphene may disrupt the cell membrane. What's more, the bending stiffness of graphene has little influence on the penetration process as graphene pierces into the cell membrane. These results provide useful guidelines for the molecular design of graphene materials with controllable cell penetrability.