A plate-welding test and a butt-welding test for Invar 36 alloy were carried out using Nd:YAG pulsed laser as welding heat source. The effects of process parameters(laser power,welding speed,pulse duration and defocus distance) on the morphology of welding joint,welding width and the penetration were analyzed and the hardness,composition and tensile strength of the fusion zone for butt-welding of 0.85 mm thick Invar sheets were tested. The results indicated that the main factors affecting the weld bead penetration, weld width and Heat Affect Zone(HAZ) are laser power and pulse duration. Moreover,the welding speed effects on the fish-scale spacing and the defocus distance on the weld bead penetration and weld width mainly. Experimental results also indicate that selecting appropriate process parameters can realize the butt-weld for the 0.85 mm thick Invar sheets in good welding modality.The composition of the welding-line has no obviously change, its tensile strength is equal to the base body and its hardness is appreciably lower than that of the base body.