The flow between two rotating concentric cylinders, also known as Taylor-Couette flow system, is one of the most widely studied systems in the classical fluid dynamics. In this work, a two-dimensional Taylor-Couette flow system is simulated using the lattice Boltzmann method combined with the smoothed profile method. The fluid flow between the rotating cylinders is solved by lattice Boltzmann equation while the curved boundaries of the cylinders are treated with a smoothed profile function. To assess the validity of the present simulation technique, three different cases of rotation of the cylinders were considered: ⅰ) inner cylinder is only rotating, ⅱ) outer cylinder is only rotating, and ⅲ) both inner and outer cylinders are rotating. For all the three cases, the numerical results of the flow velocity in azimuthal direction and the hydrodynamic torque acting on the cylinders are in good agreement with the corresponding analytical solution results.