The guiding of a laser beam in a plasma channel formed by a short ionizing pulse is investigated in the weakly relativistic limit. The plasma channel formed is axially non-uniform due to self defocusing of the prepulse. When a second delayed laser pulse propagates through the plasma channel formed by the prepulse, the competition between refraction and diffraction results into alternate convergence and divergence of the guided beam. Second-order nonlinear differential equations for the beam width parameter of the prepulse and guided pulse are derived by moment theory approach. The effect of the guided pulse and prepulse intensities on the propagation of the guided laser pulse through the plasma channel formed by the prepulse is studied. Laser guidance up to several Rayleigh lengths is observed.