The goal of the current manuscript is to investigate how a plasma density ramp affects the ability of a q-Gaussian laser beam (q-GLB) to self-focus in plasma. The laser beam exhibits oscillatory self-focusing and defocusing behaviour with increasing distance of propagation. We used an exponential plasma density ramp to combat this defocusing tendency, allowing the particular laser beam to achieve a minimal spot size and nearly retain it up to several Rayleigh lengths. In addition to that, it has been observed that self-focusing increases with increasing q-values and the laser intensity. However, the lower values of q suggest strong self-focusing. By warily selecting the plasma and laser parameters, the density ramp could play a key role in the self-focusing of q-Gaussian laser. Self-focusing is seen to become stronger as propagation distance increases and the q-parameter affects the behaviour of the beam-width parameter in the plasma as shown.