We report on a strong effect of p-GaN surface morphology on the growth mode and surface roughness of ZnO:Ga films grown by plasma-assisted molecular-beam epitaxy on p-GaN/c-sapphire templates. A range of ZnO:Ga surface morphologies varying from rough surfaces with well defined three-dimensional islands, capable to enhance light extraction in light-emitting diodes, to rather smooth surfaces with a surface roughness of ~ 2 nm suitable for vertical-cavity lasers can be achieved by controlling the surface morphologies of p-GaN. Optical transmittance measurements revealed high transparency exceeding 90% in the visible spectral range for ZnO:Ga with both types of surface morphology.