Propagation of a high power Gaussian laser beam through a plasma with a density ramp where a magnetic field is present has been investigated. The spot size of the laser beam decreases as the beam penetrates into the plasma due to the role of a plasma density ramp. The studies show that the combined effect of a plasma density ramp and a magnetic field enhances the self-focusing property of the laser beam. Both factors not only reduce the spot size of the laser beam but also maintain it with only a mild ripple over several Rayleight lengths.