High-Z (Z is an atomic number) metals are often deposited on hollow glass or polymer microspheres to improve the implosion efficiency of targets in inertial confinement fusion experiments. Smooth and crack-free thick tungsten coatings on glow discharge polymer shells have been deposited via copper doping by direct-current magnetron sputtering. Scanning electron microscopy, energy dispersive X-ray spectroscopy, X-ray diffraction, and a white light interferometer were used to characterize the microstructure, composition, phase evolution, and surface roughness of tungsten coatings. The copper atoms with appropriate amounts were found to form a supersaturated solid solution with tungsten, which can serve to refine the grains of these coatings and to smooth their surface. Copper atoms in tungsten coatings were also found to stabilize the metastable β-phase W. This β-phase W is believed to play a key role in the evolution of the size and morphology of the grains of tungsten coatings. This may become a probable method to fabricate high-Z coated targets via doping.