Laser guiding through an axially non-uniform collisional magnetoplasma channel formed by ionizing laser prepulse has been investigated. Self-defocusing of the ionizing prepulse leads to an axial non-uniform plasma channel. Due to the propagation of second laser beam through such preformed plasma channel, non-uniform heating of electrons takes place on account of non-uniform intensity distribution of laser beam. Non-uniform heating diffuses the electrons away from the axis and thereby enhances the plasma channel. Due to the competition between diffraction and refraction phenomenon through such an axial non-uniform collisional magnetoplasma channel, there is a periodic beam width variation with the distance of propagation. Second order ordinary differential equations for the beam width parameter of prepulse and the guided beam have been set up using the moment theory approach. Effect of axial non-uniformity, intensity of guided beam and magnetic field has been seen on the propagation of the second guided beam in the plasma channel.