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The lattice Boltzmann method (LBM) combined with the immersed boundary method (IBM) to simulate red blood cell (RBC) movement in micro-vessel is presented. The LBM is used to simulate the incompressible flow field, and IBM is utilized to incorporate the solid-fluid interaction. The combination keeps the advantages of LBM in simulating different kinds of flows, and provides a better approach to solve the solid-fluid boundary conditions. The RBCs are considered as liquid capsules, while the membrane is represented by a set of points that move with the fluid points, and induce external forces on the fluid by adding a force term to the lattice Boltzmann equation. The blunt velocity profiles of RBC flows are obtained, and the motion of the cell performs tumbling-rotating or tank-treading in micro-vessel. Nearly a circle of the deformation and movement of one single RBC is simulated then. Results obtained are in excellent agreement with those in the experiments.