Continuous wave (CW) Nd:YAG laser beam bead-on-plate welding of Fe-Ni (36%, mass fraction) alloy is carried out. The morphology of the cross section is analyzed by optical microscope. The influence of welding parameters (laser power, scanning speed, defocusing amount, welding angle and heat input) on the morphology of the cross section is studied. The results indicate that large negative focusing position will weaken the weldments, consequently, is of disadvantage to self-fusible welding. And the increase of laser power is more helpful to improve welding penetration than slowing down welding speed when the focusing position is fixed. The influence of the relationship between laser power and welding speed should be considered when heat input (laser power/welding speed) is used to characterize the morphology of the weld.