In this paper, we numerically investigate the relativistic self-focusing of laser beam with LG01 mode in plasmas. An effective potential is introduced to identify the critical power. Numerical methods are employed to solve the governing equations. To verify the numerical procedures, we compare the known analytical solution of the relativistic critical power for TEM00 mode with our numerical method. It is shown that there is a good agreement between our numerical results and the analytical solution. The critical power for relativistic self-focusing of a LG01 laser beam is about 6 times of that for a TEM00 laser beam
