In the 5xxx series Al-Mg alloy, magnesium addition can increase the strength of aluminum alloy by solid solution strengthening but it has a relatively low melting and boiling temperature. During full -penetration laser welding of the Al-Mg alloys, its low boiling point and high vapor pressure brings about the spiky humping bead on the bottom side. Under back-side shielding, the spiking of back bead can be reduced but it restraints the process flexibility. In this study, a square pulse waveform modulation was employed to stabilize keyhole and back bead surface without back-side shielding. By using an experimental design, the bead shapes were evaluated for various process parameters such as the focal position, welding velocity and waveform parameters and the smooth back bead shape could be achieved.