In this paper we investigate self-focusing and intensity of Gaussian laser beam propagating through the homogeneous plasma in the external tapered magnetic field. It is known that the nonlinearities effects can be acquire by the laser-plasma interaction which can lead to the self-focusing of the laser beam. By considering these nonlinear effects, equation of beamwidth of Gaussian laser beam under the paraxial approximation has been obtained and numerically solved. Results of numerical method show that external tapered magnetic field can further boost the self-focusing and localize the beam intensity. Besides, effects of cyclotron frequency, plasma density and slope constant of magnetic field parameters on self-focusing have been investigated. In addition, more results on evaluation of laser beam intensity depict that in presence of tapered magnetic field and also by increasing the slope constant parameter of the tapered magnetic field, the intensity of laser beam increases noticeably.
