A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the red blood cell (RBC) rheology in microvessels. The biconcave RBC shape in static plasma and tank-treading behavior of single cell in shear flows have been successfully captured in this model. The behavior of the RBC in a Poiseuille flow and the lateral migration of the cells in a shear flow have been investigated. It is found that the RBCs exhibit parachute shape in a Poiseuille flow with the curvature closely related to the deformability of the cell membrane and the hematocrit (Hct) of the blood. With this spring model, RBCs can recover their initial shapes associated with the minimal elastic energy when the flow stops. The simulation results also show that the RBCs migrate to the center of the domain in the radial direction in a shear flow, which clearly indicates the Fahraeus-Lindqvist effect in microvessels. The rate of migration toward the center depends on the shape of the RBC; the biconcave shape enhances this migration.