In the present study, the motion and deformation of a red blood cell in the incompressible viscous flow is simulated using the lattice Boltzmann method combined with the immersed boundary method. The lattice Boltzmann method is used to solve the flow field, whereas the immersed boundary method is used to simulate the dynamics of the red blood cell. The red blood cell is considered as an elastic boundary immersed in the fluid domain. The main advantage of the lattice Boltzmann method is that it solves only an algebraic equation. In the immersed boundary method the fluid domain is descretized using a regular Eulerian grid, while the immersed boundary is represented in the Lagrangian coordinates. The Eulerian grid points would not necessarily coincide with the Lagrangian points. The fluid- immersed boundary interaction is modeled using an appropriate form of delta function. The effects of the no-slip condition are taken into account via a forcing term added to the Navier-Stokes Equations (here the lattice Boltzmann equation). In the present study, the tank-treading motion of a red blood cell in the viscous shear flow is simulated. The results are found to be in good agreement with the available experimental and numerical ones.