Using the pulse laser beam welding-brazing technique, we form a joint between Zr44Ti11Ni10Cu10Be25 (at%) bulk metallic glass (BMG) and copper. Scanning electron microscopy with energy dispersive spectroscopy and x-ray diffraction are used to characterize the microstructures and chemical composition of the joint. There are fusion zone (FZ) and heat-affected zone (HAZ) formed across the joint. The XRD pattern of the FZ exhibits a broad diffraction halo, and no peaks of crystalline phases are present. There is a diffusion layer formed between the FZ and copper, suggesting the migration of copper towards the FZ across the FZ/Cu interface during the welding. The Vickers hardness of the joint is slightly larger than that of the BMG. The C-curve and thermal cycle curves associated with the welding are used to discuss the mechanism controlling the evolution of the structures in the FZ and HAZ.