The characteristics of zinc behavior that the zinc layer is vaporized and ionized during laser welding of galvanized steel are closely related to the stability of the molten pool, and the weld keyhole formation, easily leading to weld defects such as pores, splashes, cave, and incomplete fusion. In this paper, an experimental platform was built based on a multichannel spectrum signal acquisition to study spectral characteristics of zinc, plasma temperature, electron density, and bremsstrahlung absorption in laser welding of galvanized steel with the copper addition. The results show that, due to the formation of a copper–zinc solid solution during the laser welding of galvanized steel, the zinc content in the welding joints increased significantly. Meanwhile, by adding an appropriate amount of copper powder, the temperature and oscillation amplitude of the plasma plume during the laser welding of galvanized steel decreased significantly. Further, the inverse bremsstrahlung radiation absorption coefficient decreased, and there was less attenuation of the laser energy when passed through the plasma plume outside the keyhole. Therefore, the method implemented here improved the utilization of laser energy during welding.