In this paper, self-focusing of asymmetric cosh-Gaussian laser beams in collisionless magnetized plasma has been studied. The non-linearity in dielectric constant considered herein is mainly due to the ponderomotive force. The non-linear coupled differential equations for the beam width parameters in transverse dimensions of the beam have been obtained by using WKB and paraxial approximations under parabolic equation approach. The numerical computation is completed by using fourth-order Runge–Kutta method. The effect of unlike decentered parameters in both transverse dimensions of the beam on self-focusing of cosh-Gaussian beams has been presented. Further, the effect of the static magnetic field and polarization modes of the laser has been explored.