Numerical simulations are performed to examine the packing behavior of human red blood cells (RBCs). A combined finite-discrete element method (FDEM) is utilized, in which the RBCs are modeled as no-friction and no-adhesion solid bodies. The volume-to-void ratio of a large number of randomly packed RBCs is clarified, and the effects of the RBC shape, the mesh size, the cell number, and the container size are investigated. The results show that the packed human RBCs with normal shape have a void ratio of 28.45%, which is slightly higher than that of the flat or thick cells used in this study. Such information is beneficial to the further understanding on the geometric features of human RBCs and the research on RBC simulations.