Experiments of laser lap welding of two 1.2 mm thick galvanized steel planks with different Cu powder concentrations were performed by using a 4 kW fiber laser. The transverse weld topography, the mechanical properties, fracture morphology, component distribution and the main phase of the welded joint regional were studied under the optimal welding process parameters acquired through process optimization. It is shown that, when Cu powder concentration is 2.82%, the average tensile strength and elongation of the welding joints is 382.5 MPa and 32.5% respectively. When Cu powder concentration is not more than 3.46%, the tensile specimens are broken in the base material due to ductile fracture. On the contrary, the tensile specimens are broken in weld area due to the mixture of predominant ductile fracture and subordinate brittle fracture. Element distribution and phase in the galvanized steel interface are changed with the addtion of Cu powder added. In the weld area, the width of mixing zone of C, Al, Mn, Fe, Zn, Cu elements is larger. When Cu powder concentration is 2.82%, Cu element changes stably and Cu element in the weld area plays an important role in solid fusion reinforcement with the formation of Cu-Zn solid solution, and therefore, the strength of the weld area is improved. When Cu powder concentration is 8.06%, Cu element may spread from weld area to heat affected zone and is therefore prone to form brittle intermetallic compound Cu5Zn8, making specimens easily fractured in the weld area.