The single crystals form the foundation of the modern technology. They are needed for the scientific appraisal of crystallography, topography and tensor properties of all crystalline materials. The Czochralski technique is one of the widely used prototypical systems for melt-crystal growth. The modeling and understanding of the heat and mass transfer have become an important issue in the optimization of Czochralski technique to grow more uniform and better-quality crystals. In this paper, an alternative new method, Lattice Boltzmann Method (LBM), was used for the simulation of flows in CZ crystal growth. However, the standard LBM can only be used in the Cartesian coordinate system. By inserting the position, time and particle velocity dependent source terms into the evolution equation, the standard LBM can be transformed to be used in the cylindrical coordinate system. We extended this idea to solve the axisymmetric benchmark problem suggested by Wheeler for CZ crystal growth, avoiding the use of 3D standard LBM. The results compared well with available data in the literature.